Calculus Questions

Use the Second Fundamental Theorem of Calculus to find F x X 1 E 3 dt 4 7 F x F x

Evaluate the definite integral 649 e 36 Submit Answer dx xv In x

Evaluate the definite integral x 1 2x 4 dx

Evaluate the indefinite integral e7x 12042 e7x 2 dx C

Evaluate the indefinite integral 1 COS X 18 sin 8 x dx

Evaluate the indefinite integral 1 sec 30 tan 30 de C

Since u 2 3x then converting back to an expression in x we get the following Remember to use absolute values where appropriate Inl Injul C

Now if u 2 3x then dx xx du 1 du 2 3x This evaluates as the following Remember to use absolute values where appropriate 11 du

Step 1 We must decide what to choose for u If u f x then du f x dx and so it is helpful to look for some expression in missing a constant factor We see that 2 3x is part of this integral and the derivative of 2 3x is dx for which the derivative is also present though perhaps 3x dx 20 x 3x 2 2 3x which is simply a constant

Since u 8 x then converting back to an expression in x we get 1 c 28 C

Now if u 8 x4 then This evaluates as x s dx us du 1 us du 8 x4 6 dx

x 18 We must also convert x dx into an expression involving u If u 8 x is substituted into x 8 x4 6 dx then we have We know that du 4x dx and so x dx du x u dx x x3 U6 x dx

Evaluate the integral by making the given substitution x 8 x 6 dx u 8 x x4 6 Part 1 of 4 We know that if u f x then du f x dx Therefore if u 8 x4 then du Orchmit Skin you coppet come back dx

Determine the convergence or divergence of the series If you need to use co or 00 enter INFINITY or INFINITY respectively n 1 4n 1 lim no 3n 1 converges diverges 1 4n 1 3n 1 4 3

Evaluate the integr l by making the given substitution Je 4x 4x dx U 4x

Find the average value of f x 2 Vx 1 X 1 x 6

Find the average value of f x x 1 15 x 6 s X

The linear density p in a rod 7 m long is 12 X 9 Pave kg m where x is measured in meters from one end of the rod Find the average density Pave in kg m of the rod kg m

Evaluate the integral using the indicated trigonometric substitution Use C for the constant of integration 4x 25 O CHOICE C Sketch and label the associated right triangle CHOICE A X 0 dx 4x 25 0 5 X 5 X sec 8 2 5 X 4x 25 CHOICE B CHOICE D O 2x 5 4x 25 5 4x 25 2x

Evaluate the integral 0 6 x2 9 25x2 dx

Find the average value of f on 0 16 1 0 4 100 8 12 AX

Consider the following function x x 3 a Determine an appropriate trigonometric substitution O Use x 3 sin 0 where 1505 12 24 0 since the integrand contains the expression x 3 I 2 dx O Use x 3 tan 0 where 3 T dx T O Use x 3 sec 0 where 0 0 or 0 2 TC 2 0 since the integrand contains the expression x2 3 V 2 b Apply the substitution to transform the integral into a trigonometric integral Do not evaluate the integral x x2 de 37 since the integrand contains the expression x2 3 2

Consider the following function x6 dx 1 x a Determine an appropriate trigonometric substitution Use x Use x sin 8 where tan 8 where T T 0 since the integrand contains the expression 1 x 2 2 dx T T 0 since the integrand contains the expression 1 x 2 2 Use x sec 0 where 0 0 or 0 since the integrand contains the expression 1 x V 2 3 2 b Apply the substitution to transform the integral into a trigonometric integral Do not evaluate the integral de

sin x Since cos x is the derivative of sin x then 12 sin x cos x dx can be done by substituting u Step 4 With the substitution u sin x we get 12 12 sin x cos x dx 12 u du 12 which integrates to C X Substituting back in to get the answer in terms of sin x we have S 12 sin x cos x dx C

The series True O False 00 n 0 n 2 1 converges

lim 0 converges O diverges convergence or divergence of the series If you need to use coor co enter INFINITY or INFINITY respectively

Tutorial Exercise Evaluate the integral 1 Step 1 12 sin x cos x dx Since S 12 sin x cos x dx has an odd power of of cos x we will convert all but one power to sines We know that cos x sin x

Evaluate the integral 4 0 sin5 x dx

1 Determine function f x x Power series for the

converges conditionally converges absolutely diverges Need Help Submit Answer nwi Read It 6 25 6 25 Points Determine whether the series converges absolutely or conditionally or diverges COS n Watch It n DETAILS PREVIOUS ANSWERS LARCALCET7 9 5 057

Find the average value of f on 0 16 y 1 0 t 8 12 4X

An alternating series always converges True False

College students were given three choices of pizza toppings and asked to choose one favorite The following table shows the results Find the probability that the favorite topping is meat given that the student is senior 0 194 O 0 283 0 469 O 0 085

How many four digit passcodes are possible if the first digit can not be five and repetition is not allowed Write the answer as a whole number

In a statistics class there are 23 juniors and 19 seniors 9 of the seniors are females and 15 of the juniors are males A student is selected at random Find the probability of selecting a junior or a female 32 42 28 42 O 24 42 34 42 O 30 42

Two dice are rolled one time Find the probability of getting a sum of 6 or doubles O 10 36 11 36 O 12 36 9 36 13 36

A couple has three children Find the probability of getting two boys 18 48 0 3 8 05 8

Two coins are tossed one time Find the probability of getting one head O 2 1 8 4

Two cards are drawn with replacement from a deck of cards Find the probability of selecting a king and a face card in order 0 083 O 0 143 0 018 0 374 0 247

Two marbles are drawn without replacement from a box with 4 blue 3 white and 2 red marbles Find the probability of selecting a blue and a red marble in order 0 111 O 0 486 O 0 591 0 227 0347

Problem 54 Find the intervals on which f x is increasing the intervals on which f x is de creasing Then sketch the graph Add horizontal tangent lines f x x 3x 3x f x x 3x 3x

In a certain college 33 of the physics majors belong to ethnic minorities Find the probability of the event from a random sample of 7 students who are physics majors exactly five belong to an ethnic minority 0 037 0 147 0 274 O 0 085 0 015

A student takes a multiple choice test of 10 questions with four choices and guesses on each question Find the probability that the student gets exactly 7 correct answers 0 183 O 0 047 O 0 029 0 003 0 015

Find the exact length of the curve y 2 3 1 4 2 3 10 3 1 x 2 0 x 5

There are 10 members on a board of directors If they must elect a chairperson a secretary and a treasurer how many different slates of candidates are possible Write the answer as a whole number

A symphony decides to raise money by raffling off an oven worth 500 a dinner worth 170 and a set of books worth 125 A total of 2000 tickets are sold at 2 each After each prize drawing the winning ticket is returned to the pool of tickets Find the expected value of winning for a person who buys 1 ticket in the raffle 1 38 O 1 25 O 1 75 O 1 95 O 1 60

A bag contains 5 cherry 2 orange and 3 lemon candies You reach in and take 3 pieces of candy at random Find the probability of selecting 1 orange and 2 cherry 0 385 0 274 0 047 0 495 0167

There are 8 women and 6 men in a department A committee of six people is to be selected How many different ways can the committee be selected if there must be 3 women and 3 men 12 720 3850 076 O2780

A shirt company has 5 designs each of which can be made with short or long sleeves There are 8 color patterns available How many different types of shirts are available from this company Write the answer as a whole number

Find the future value of the loan Round the answer to the nearest dollar 9570 at 4 35 for 8 years