Definite Integrals Questions and Answers

Write and simplify but do not evaluate an integral with respect to x that gives the length of the following curve on the given intervall y 5 cos 3x on SIRET TT 2 4 An integral that gives the arc length is dx COLDS

Find the remaining trigonometric ratios of 12 and terminates in QI 22 13 21 cos 0

Let R be the region bounded by the following curves Let S be the solid generated when R is revolved about the given axis If possible find the volume of S by both the disk washer and shell methods Check that your results agree 1 9 y x y x in the first quadrant revolved about the x axis Set up the integral s that gives the volume of the solid as a single integral if possible using the disk washer method Use increasing limits of integration Select the correct choice below and fill in any answer boxes within your choice OA dx Type exact answers C B dx dx Type exact answers

2 Evaluate a sin T b cos 0 c tan 5 d sin 45

Let R be the region bounded by the following curves Use the shell method to find the volume of the solid generated when R is revolved about the y axis y 8 x y 0 x 1 and x 3 Set up the integral that gives the volume of the solid using the shell method Select the correct choice below and fill in the answer boxes to complete your choice Type exact answers OA B 1 3 1 dy 2x 8 x 0 dx The volume is Type an exact answer

Let R be the region bounded by the following curves Use the shell method to find the volume of the solid generated when R is revolved about the x axis y x y 0 and x 25 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 an exact answer OA Sax dx OB dy y x

Question Find the total area between the curve of the function f x x 1 and the x axis over the interval 9 5

Question What is the net signed area between f x 2x 2 and the x axis over the interval 8 5 Do not include any units in your answer Provide your answer below IE

Find the net signed area between the curve of the function f x 2x 4 and the x axis over the interval

CURRENT OBJECTIVE Use substitution to evaluate a definite integral with the power rule Question Find d 3x 3x 2 dx Enter your answer as an exact fraction if necessary

CURRENT OBJECTIVE Use substitution to evaluate a definite integral with the power rule Question Evaluate the following definite integral 5x x 1 dx Enter your answer as an exact fraction if necessary

Find the volume of the solid generated by revolving the region bounded by y 2x y 0 and x 3 about the x axis Set up the integral that gives the volume of the solid S 0 dx GEER

Question Find x x 1 dx Submit your answer in fractional form Provide your answer below

Question 4x Include the constant C in your answer Evaluate 4x 1 2x x 3 4 dx Provide your answer below

Math 124 4 Find if any the horizontal asymptotes of the following functions and use that information to match them with their graphs on the next page Each question should have two limit computations with and r o x 1 4 a f x r 3x 7x 10 Worksheet x 3 b f x 2 8x 26 c f x x 4x 9 x 4

Find the total distance traveled by a particle given its velocity function Question Find the total distance traveled by a particle according to the velocity function v t 4t 6 m sec over the time interval 0 5 Enter your answer as an exact fraction if necessary and do not include units in your answer

For the region bounded by y 3x the x axis and x 5 determine which of the following is greater the volume of the solid generated when the region is revolved about the x axis or about the y a When the region is revolved about the x axis the volume is Type an exact answer using as needed Points 0 of 1 I

Find the volume of the solid generated when R shaded region is revolved about the given line y 18 x y 18 x 324 about y 18 The volume of the solid obtained by revolving th

Find the volume of the solid generated when the region bounded by y 4x and y 12 x is revolved about the x axis Set up the integral that gives the volume of the solid 10 dx CID YA

Use part I of the Fundamental Theorem of Calculus to find the derivative of 8x u 5 g x du u 3

Find the volume of the solid generated when the region bounded by y 2x and y 4 x is revolved about the x axis Set up the integral that gives the volume of the solid dx

ind the volume of the solid generated when the region bounded by y 3x and y 6 x is revolved about the x axis Set up the integral that gives the volume of the solid To 0 dx y 6 x y 3

Find the volume of the solid generated when the region bounded by y 3x and y 12 x is revolved about the x axis Set up the integral that gives the volume of the solid 9

Question Find the total distance traveled by a particle according to the velocity function v t 4t 4 m sec over the time interval 0 4 Enter your answer as an exact fraction if necessary and do not include units in your answer Provide your answer below

Find the volume of the solid generated by revolving the region bounded by y 2x y 0 and x 3 about the x axis Set up the integral that gives the volume of the solid 10 dx 0 1 epowers CIT

Question 2 If 8 f x dx 3 and S f x dx 2 what is the value of P f x da 8 5

Question Determine the value of S Provide your answer below fox f x dx given that 6 f x dx 9 and f x dx 3

Question Given that a particle travels according to the velocity function v t 2t 7 m sec what is the total distanced traveled by the particle over the time interval 2 5 Enter your answer as an exact fraction if necessary and do not include units in your answer

Question Calculate the area in square units bounded above by f x 7x 2x 20 and below by g x 8x 15x 2 Provide answer holour

Question Consider the region bounded above by f x 2x 9x 10 and below by g x x 12x 10 Find the area in square units between the two functions Provide your answer below

A particle travels according to the velocity function shown below where velocity is measured in meters per second Find the net displacement of the particle for the first 5 seconds if 0 t 2 if 2 t 5 Enter your answer as an exact fraction if necessary and do not include any units Provide your answer below 7 O v t 2 3t 4 2

Question Given that a particle travels according to the velocity function v t 4t 8 m sec what is the total distanced traveled by the particle over the time interval 0 7 Enter your answer as an exact fraction if necessary and do not include units in your answer Provide your answer below I

Question Determine the area in square units of the region bounded by g x 10x 11 and f x x 5x 13 over the inter

Question Determine the area in square units of the region bounded by g x 7x 7 and f x x 11x 28 over the interval 3 7 Provide your answer below

Use part I of the Fundamental Theorem of Calculus to find the derivative of F x 0 INOTE Enter a function as your answor F x f sin sin t dt

Given At what value of x does the local max of f x occur X t 1 f x 1 cos t dt

A hemispherical bowl of radius 6 inches is filled to a depth of h inches where 0 sh 6 Find the volume of water in the bowl as a function of h Check the special cases h 0 and h 6 th 18 h in3 3 The volume of the water in terms of h is Type an exact answer using as needed What is the volume of water when h 0 V 0 Simplify your answer Type an exact answer using as needed Use integers or fractions for any numbers in the expression

Question 2x What is the value of 8cos x sin x dx Provide your answer below

Question What is the value of 7x 6 1 24cos x sin x dx Sorry that s incorrect Try again

0 1 6 e x e x sec e x dx Round your answer to 3 decimal places Evaluate Provide your answer below

Keep your answer in rational form do not approximate Find Dr sin in x dx or bol

Question Find the area in square units bounded above by f x 6x 2x 19 and below by g x 7x 12x 21 Provide your answer below

Find the volume of the solid formed when the region bounded by the graph of f the x axis and the line x 5 is revolved about the x axis if 0 x 3 if 3 x 4 3x 18 if 4 x 5 X f x 3x 6 CELE 104 5 0

A hemispherical bowl of radius 6 inches is filled to a depth of h inches where 0sh 6 Find the volume of water in the bowl as a function of h Check the special cases h 0 and h 6 The volume of the water in terms of h is in Type an exact answer using as needed

1 point A bacterial colony increases in size at a rate of 4 899e 55t bacteria per hour If the initial population is 88 bacteria find the population 3 hours later Population is bacteria

1 point Find the derivative of the function g x g x 9t 6t dt

1 point Evaluate the integral 0 3 8x 1 dx

1 point Evaluate the integral 0 20 5 Z dz

1 point Evaluate the integral 2 x 3 1 x 3 dx

1 point Evaluate the integral 1 2 14 dt