Definite Integrals Questions and Answers

Find the average value of the function f x 4x on the interval 2 x 4

Evaluate answer S cos z ln 1 24 1 1 1 82 39 9 dr Question Help OVideo Message instructor

15 points Compute the following double integral e 5x 4xy 5y JR2 2

Simplify 1 cot x sin x cos x cos x x

Using cylindrical coordinates evaluate the triple integral III 2 x y 8m where W is the cylindrical solid centered around the z axis and bounded by the cylinder z2 y 4 and th horizontal planes z 2 and 23 The answer is an integer in this case Enter this value below Do not use decimal points Triple integral

So 1 1 x dx 1 1 201 a 1 dx 1 x O

11 f t 1 5 g t 21 3 Find f g 1 13 h n 3n 2 g n 3n 2 Find h g n 15 h x 3x 4 g x 3x 3x Find h g x

Rationalize the denominator 18 1 2

Evaluate the given integral by changing to polar coordinates 11x x y2 dA where D is the region bounded by the semicircle x V64 y2 and the y a

ndicate whether the table specifies a function Range 14 Domain 8 13 8 13 SEHEE LACERES H EMENE I 6 16 2

Evaluate each definite integral below using the fundamental theorem of calculus and substitution 1 L V x 1dr Hint Rewrite 2 1 r 1 2 and then use u substitution 1 k Tea dx 3 I dr

Evaluatex 2 dx A 1 B 2 C 3 D 4

Using the graph of f x evaluate fro f x dx A 10 7 B 10 7 C 11 3 D 11 9 1 5 2 1 0 y f x Area 11 3 Area 0 6

Evaluate the following definite integral using a geometric formula You must show all work including the geometry area formula 1 1 x dx A B 2 C 3 D 4

Evaluate the integral below by interpreting it in terms of areas in the figure The areas of the labeled regions are A1 6 A2 4 A3 1 and A4 1 V V 7 2f x dx 10 A1 y f x 3 A2 5 A3 7 A4 figure is NOT to scale 4

OA OB Oc a t ft sec 5 2 The data for the acceleration a t of a car from 0 to 6 seconds are given in the table above If the velocity at 7 0 is 11 feet per second the approximate value of the velocity at 7 6 computed using a left hand Riemann sum with three subintervals of equal length is A 26 ft sec B 30 ft sec C 37 ft sec D 39 ft sec OD 8 3 E 41 ft sec Office Online Fr

If f x g x 7 for 3 x 5 then x g x A 21 g x dx 7 B 2 g x dx 14 3 C 2 g x dx 28 D g x dx 7 E g x dx 14 OA B Oc OD 19

The graph shown below is f x 2x 2 If g x f t dt what is g 2 f 543 2 1 2 3 4 5 O 0 o 2 O2 52345 04 2 3 33 3

a b c are reals numbers a b 1 C

A 1 The graph of a piecewise linear function f for 1 x 4 is shown above What is the value of If x dx OA OB Oc OD 1 0 1 B 2 5 C 4 3 D 5 5 E 8

B Use the Trapezoidal Rule the Midpoint Rule and Simpson s rule to approximate the integral 3 1 50 with n 8 T8 M8 S8 In x 3 x dx Report answers accurate to 4 places Remember not to round too early in your calculations

dv Draw a dependency diagram and write a chain rule formula for where v g p q p k m q h m dm Choose the correct dependency diagram below O A OB P v g p q dv op dp dm m du dq q dq dm p m dv dp SICCEM v g p q op dm p p q dq dm dv dq q m OC 318 v g dv dg P

The corner points of a bounded feasible region are 0 0 0 2 1 5 0 and 1 2 1 2 Determine the maximum value if any of the objective function z 4x 3y Maximum value of z is 8 4 No Maximum Maximum value of z is 12 8 Maximum value of z is 16 4

Approximate the area A under the graph of the function f x xe by partitioning 1 8 into 20 subintervals of equal length and using an upper sum Use decimal notation Give your answer to two decimal places

Decide whether the statement is true or false 0 x x is a natural number less than 5

00 1 dx converges O diverges 19 09 Points 00 n 1 1 1 0 5 dx Use the Integral Test to determine the convergence or divergence of the p series dx O converges DETAILS 1 0 9 n Viewing Saved Work Revert to Last Response LARCALCET7 9 3 031 0 15 Submissions Used

find the F CSx 3 dx A integral 25x 9x c B 3x 9x c x 15x 79X C D 253 15x 479x C

When you have done this concept assignment into the text box type the equation s for the piecewise function whose graph is shown below and then click Submit Assignment Hint the pieces in this piecewise defined function are from the library of common functions we ve already studied y 2

Evaluate the definite integral 8x1 3 dx

Let S be the part of hemisphere x y z 4 in the first octant Compute fxz ds S

Evaluate the definite integral 7 u du

Evaluate the definite integral 18 27 3 IN

A bucket begins weighing 30 pounds including the sand it holds The bucket is to be lifted to the of a 25 foot tall building by a rope of negligible weight However the bucket has a hole in it and leaks 0 3 pounds of sand each foot it is lifted Find the work done lifting the bucket to the top of the building foot pounds Question Help Video Message instructor

Let A z f t dt where is the function given by the graph f bel 25 0 5 3 4 A 4 3 4 A 6 A 9 Question Help Video Message instructor Calculator 00 9 q

Find the area between the curves y e 0 32 and y 1 3x 1 from x 0 to x 3 Area

Sv If q z V15 dr then Question Help Video Message instructor

Evaluate 3 dz EN PE Vidar 1 Tvideo D Meccan

The CIA published data about foreign countries on its web page In particular they show total population as well as population growth If a student is looking at Russia they will see that the total population of Russia is declining When they look at the table that shows annual population growth all the rates are positive Assume population grows and declines at a rate proportional to the population What is the problem

Jane is taking a history class The teacher states that the population of a country is shrinking at a rate proportional to the population at a given time and describes the size of the population as P 10e SUP 0 5t SUP where t is years Is this possible N

Given the function graphed below evaluate the definite integrals 4 3 2 1 Hiv 1 3 4 8 1 S f x dx f x dx 2 LAD 3 4 5 10 Question Help Video Message instructor 7 8 a

Graph the polar equation Identify the name of the shape 40 r 4 sin 50 a Identify the shape rose curve b Identify the number of petals 20 X c Identify the length of each petal 7 d For what values of 0 within 0 2x mark the maximum value of Ir e Plot the tip of each petal below no need to connec them n

Find f f 0 f e sin e cos 8 f 0 4 f 0 1

The table below shows values for four differentiable functions Suppose we know the following things c x b r b x p x p x t x t x c z b z 0 t x 0 c x p x What is 0 1 What is 1 is f c Sp z dx 14340 2210m 31222 4 2 Answer y 3 c x 4 dx 4 3434 What is the equation of the tangent line to the curve y t z when z 3

Given L definite integral that is provide a b and f x in the expression a 7 4 1 8 4 1 b express the limit as n as a f x dx

A a B b a b The graph of f is shown in the figure above If g x f t dt for what value of x does g x have a maximum OA OB t Oc OD Vax D d E It cannot be determined from the information given Office Online Fra

f x 10 30 40 20 The function f is continuous on the closed interval 2 8 and has values that are given in the table above Using the subintervals 2 5 5 7 and 7 8 what is the trapezoidal approximation of x x A 110 OA OB Oc C OD B 130 C 160 D 190 E 210 Office Online Fra

Let exy 5z 2 7 e 22 5 7 5z e Calculate the flux of one edge along the positive y axis one edge in the xz plane with x 0 z 0 H dA through the square of side 2 with one vertex at the origir and the normal 7 7 k

All ions are electrolytes because they can conduct an electrical current in solution True False Question 5 2 points Listen Which of the following statements is FALSE Chemical reactions progress at a faster rate when the reacting particles are present in higher numbers Chemical reactions proceed more quickly at higher temperatures Catalysts increase the rate of chemical reactions sometimes while undergoing reversible changes in shape Larger particles move faster than smaller ones and thus collide more frequently

of x 3 dx O No f x x 3 dx is not continuous on the given interval but its antiderivative exists x 9 Yes f x f dx is continuous on the given interval but its antiderivative does not exist x 3 Can the Fundamental Theorem of Calculus be used to find O No f x Yes f x f x 3 dx is not continuous on the given interval and its antiderivative does not exist x 3 dx is continuous on the given interval and its antiderivative exists 24 25 26 27 28 29 30 31 32 33 Next

Solve the following equation for 0 x I SZE X sin x cos 2x Evaluate the integral and interpret it as the area of a region 15 sin x 5 cos 2x dx Sketch the region O y X y no 2 4