Definite Integrals Questions and Answers

1 point Evaluate the integral 3x dx

1 point Evaluate the integral 5 Lo 0 y 6 2y 7 dy

1 point Evaluate the integral T 3 T 4 sec x tan x dx

Enonc D terminer les entiers relatifs n tels que n 4 divise 3n 17

Use the general slicing method to find the volume of the following solid The solid whose base is the triangle with vertices 0 0 2 0 and 0 2 and whose cross sections perpendicular to the base and parallel to the y axis are semicircles Set up the integral that gives the volume of the solid Use increasing limits of integration Select the correct choice below and fill in the answer boxes to complete your choice Type exact answers O A OB dx dy

Find the remaining sides of a 45 45 90 triangle if 49 The shorter sides are each 1 51 The shorter sides are each 4 53 The longest side is 8 2 55 The longest side is 4 50 The shorter sides are each 5 52 The shorter sides are each 54 The longest side is 5V 2 56 The longest side is 12

salon sells its cologne wholesale for 4 75 per bottle The variable costs of producing x thousand bottles is 3x 2420x 325 dollars and the fixed costs for manufacturing are 170 0 Expressions for the revenue cost and profit from selling x thousand items Which expression represents revenue YA R 4750x C R 4 75x Which expression represents cost A C 3x 2420x 169 675 C C 3x 2420x 169 675 Which expression represents profit A P 3x 2330x 169 675 OC p 3x 2330x 169 675 S OB R 4 75x 170 000 OD R 475x OB C 3x 2420x 170 000 OD C 4750x 170 000x O B P 3x 7170x 170 000 OD P 3x 7170x 169 675

Question Find the net signed area between the curve of the function f x 2x 4 and the x axis over the interval 7 3 Do not include any units in your answer Provide your answer below

Question Provide your answer below SAT Y 5 4 3 2 1 3 6 g x 9 f x 4x x g x 4 x 8 h x 216 30x x 12 h x 15 18 x Use the formulas for areas of triangles and circles to evaluate the integrals of the functions graphed in the figure Enter the sum of all shaded areas in terms of

6 Evaluate Ix 41 dx using a geometric formula Provid

1 point Use the midpoint rule with n 4 to approximate the integral 6 C x dx

1 point The table below gives the values of a function obtained from an experiment x f x Using three equal subintervals with left endpoints 2 f x dx Using three equal subintervals with midpoints 2 f x dx 6 3 1 7 2 1 Use the values in the table to estimate x dx in three different ways Using three equal subintervals with right endpoints f x dx 8 0 7 9 0 5 10 1 5 11 12 3 2 3 9 Suppose that f x is known to be an increasing function Will your estimate using right endpoints be an overestimate or an underestimate for the exact value of the integral Will your estimate using left endpoints be an overestimate or an underestimate for the exact value of the integral Will your estimate using midpoints be an overestimate or an underestimate for the exact value of the integral underestimate

1 point If f x dx 16 6 and f f x dx 4 8 find f x dx f x dx m B

Previous Problem 1 point Given that 0 Problem List Next Problem 16 27x 36 dx 2628 292 1944 calculate S 27 u 36 du 16 27u u 36 du

1 point Evaluate the integral by interpreting it in terms of areas 2 4x dx

Find a function f and a positive number a such that f x a f f t dt 2 2 dt 6x

graph of a function y f x is given below Evaluate the following integrals by interpreting them in terms of areas 3 12 1 12 co 3 y f x 5 10 6 7 4 f 2 dz O S4 4 f x dx 10 S 4 4 f x dx 8 9 10

The following limit is a definition of f a Determine the function f x and the value of a 4 h 4 h TH lim h 0

Use limits to compute f x f x 1 13x f x

Let f x be a continuous function for which we know f 1 1 f 4 4 f 1 4 and f 4 16 Find the value of the definite integral gi f x z f x 1 dz a 2 2 2 1 dz Note as always do not round your answers

Let f x be a function with first order derivative f x second order derivative f x etc We know that So f x da 7 and f 0 1 f 1 2 f 0 3 f 1 4 f 0 5 f 1 6 Determine A 2 B 1 C 0 D 1 E 2 f x x dx

What is the net signed area between f x 2x 5 and the x axis over the interval 1 6 Do not include any units in your answer

Find the area of the region described The region in the first quadrant bounded by y 5 and y 5 sin x on the interval The area of the region is Type an exact answer using x as needed T

Find the area of the shaded region shown in the figure which is not shown to scale COL

Given the function f x 4x 8 find the net signed area between f x and the x axis over the interval 5 6 Do not include any units in your answer Provide your answer holow

Use the figure and any appropriate relationship s among circular functions to find the value tan 5x 6 Select the correct choice below and if necessary fill in the answer box to complete your choice O A 5x 6 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression OB The expression is undefined tan 12 12 1 13 22 12 12 7 3x 5x4 6 1 0 7x 13 2x 65x 4 w 4x 3 Ay 0 1 5x 3 4 I 60 11x 1 0 7x6 4 0 1 3x 2 x y 1 N

Determine the area of the shaded region in the figure 10 O C S x 15 15 dx What is the area of the region in terms of y 0 5 OA 2y dy 1 15 dy 12v 0y 3 0 5 OC 15 2y dy 3 5 2 The area of the shaded region is 2y 15 dy x y 15 x 2y 15 D 2 B 6 x 15 dx 15 5 3 10 10 x 16 2 X S dx 6 2y y 15 dy 15 OD 2y y 15 dy 24

Determine the area of the shaded region in the 6 10 I V x 15 dx x 15 2 dx 15 6 OA O C 10 x 15 2 dx 15 What is the area of the region in terms of y 0 OA 2yc 3 5 5 j 1 16 2y dy dy OC x 15 2y dy The area of the shaded region is Type an exact answer x y 2 15 x 2y 10 15 OB 2 x 15 d dx 10 1 6 6 D 2 2 x 15 dx x 15 15 B 2y 15 dy 3 10 OD 2y 15 dy 15 dx

Express the area of the following shaded region in terms of a one or more integrals with respect to x and b one or more integrals with respect to y a What is the area of the region in terms of x 10 OA x 10x dx 5x 50 dx 5 0 5 10 OB 10x dx 5x 50 dx 5 0 5 10 OC f x 15x 50 dx 2 10 OD x 15x 50 dx 10x y 5x 50

Determine the area of the shaded region in the figure OA S 4x x 5 dx 5 1 0 S x 5 dx S 4x dx 5 1 What is the area of the region in terms of y 1 OA y 5 dy 1 0 S 1 dy 1 OC y 5 dy 4 0 S dy 1 The area of the shaded region is Type an exact answer y 4x y x 5 OU C OB OD B 5 1 5 x 5 4x dx x 5 dx 1 j x 6 2 oy dy y 5 dy 4x dx

Find the area of the shaded region shown in the graph CEL 20 y 20 sinx y 20 cos x KIN

90 horsepower outboard motor at full throttle will rotate its propeller at exactly 4500 revolutions per min Find the ngular speed of the propeller in radians per second 500 rev per min radians per sec Round to the nearest tenth as needed

Evaluate the indefinite integral S xl x 4 5x dx

1 1 5 sec

Use the Evaluation Theorem to decide if the definite integral exists and either evaluate the integral or enter DNE if it does not exist 57 Lot secx tan x dx

Evaluate the definite integral 4 1 6 5x dx 0

5 15r Gr

Convert the following degree measure to radian measure 87 87 radians Type an integer or a decimal Round to the nearest hundredth

Perform the calculation 69 12 52 42 69 12 52 42 0 Simplify your answers Type an integer or a fra

Determine the area of the shaded region in the figure What is the area of the region in terms of x 6 OA x 15 dx 15 10 OC S x 15 15 10 S x 15 6 dx dx x y 15 x 2y Q o G COLLE OB Points 0 c 10 S 22 x 15 dx 15 6 10 D 2 f x 15 dx f x 15 15 6

Determine the area of the shaded region bounded by y x 4x and y x 2x 30 20 10

Find the area of the region in two ways a Using integration with respect to x b Using geometry a Using integration with respect to x what would be the appropriate integral to find the area 10 OA 10 4 10 x x 4 dx 3 OB 2 10 x dx 2 10 x 0 OC 2 3 2 f x 4 dx 0 3 OD 10 x x x 4 dx 10 8 6 4 2 Ay 0

What is the difference between lim f x The limit as x approaches 3 and f 3 Z 3 B i US X x S EEE

For this question you should type which formula you should use simple compound annuity payout annuity loan You should also tell me which variable you will be solving for and you should type your final answer to two decimal places ALL OTHER WORK MUST BE ON PAPER YOU SEND TO ME so I can see you substituted into the equation properly and the steps you took to solve I need to know how much money will I need to have at retirement so I can withdraw 75 000 a year for 23 years from an account earning 4 compounded annually a How much do you need in your account at the beginning b How much total money will you pull out of the account c How much of that money is interest Formulas

A simple model for the flow of air in and out of the lungs of a certain mammal is given by the following equation where V t measured in liters is the volume of air in the lungs at time t 0 t is measured in seconds and t 0 corresponds to a time at which the lungs are full and exhalation begins Only a fraction of the air in the lungs is exchanged with each breath The amount that is exchanged is called the tidal volume Complete parts a through c below V t sin 2 1 2 A V t V 0 v x dx 0 b OC V t V 0 v t dt V t 13 cos Find the volume function V assuming that V 0 14 L a at 2 Type an exact answer b What is the breathing rate in breaths minute The breathing rate is 15 breaths minute Type an integer or a simplified fraction c What is the tidal volume and what is the total capacity of the lungs The tidal volume is 7 3 2 liter s t OB V 0 V t t v x dx 0 b OD V 0 V t V t dt a

Consider an object moving along a line with the following velocity and initial position v t 16 1 on 0 5 s 0 3 Determine the position function for t20 using both the antiderivative method and the Fundamental Theorem of Calculus Check for agreement between the two methods To determine the position function for t20 using the antiderivative method first determine how the velocity function and the position function are related Choose the correct answer below OA The position function is the absolute value of the antiderivative of the velocity function OB The position function is the derivative of the velocity function OC The velocity function is the antiderivative of the absolute value of the position function D The position function is the antiderivative of the velocity function Which equation below will correctly give the position function according to the Fundamental Theorem of Calculus b OA s t s 0 v t o Sv t dt C a t OC s 0 s t v x d v x dx 0 b fv t dt OB s t v t a OD s t s 0 t v x dx 0

Consider an object moving along a line with the given velocity v Assume t is time measured in seconds and velocities have units of m S a Determine when the motion is in the positive direction and when it is in the negative direction b Find the displacement over the given interval c Find the distance traveled over the given interval v t 212 16t 30 0 6 a When is the motion in the positive direction Select the correct choice and if necessary fill in the answer box to complete your choice OA The motion is in the positive direction for t values in the interval s Use a comma to separate answers as needed Type your answers in interval notation OB The motion is never in the positive direction

For the following exercises the position function of a ball dropped from the top of a 200 meter tall building is given by s t 200 4 9t where position s is measured in meters and time t is measured in seconds Round your answer to eight significant digits 16 T Compute the average velocity of the ball over the given time intervals a 4 99 5 b 5 5 01 c 4 999 5 d 5 5 001 17 Use the preceding exercise to guess the instantaneous velocity of the ball at t 5 sec

Evaluate int 1 3 y d x where the values of y at regular intervals of are given as follows Table 13 3 begin tabular hline 1 2 3 4 5 6 7 8 91 hline x 1 0 1 25 1 50 1 75 2 00 2 25 2 50 2 75 3 00 hline y 2 45 2 80 3 44 4 20

Evaluate the definite integral 6 x 5x dx