Indefinite Integration Questions and Answers

Evaluate the integral 541 Vi 5 t dt dt

Use substitution to find the indefinite integral 3 fax x x dx 3x 2x dx

Use substitution to find the indefinite integral 30x5 dx 6 2 5x 5 S 30x 2 5x dx 6

Use substitution to find the indefinite integra p p 2 dp p p 2 dp

Evaluate the integral 8e8t f 5 e8t 8t 8e 8t dt dt

Find the integral 2 x 1 e4x 1 e4x 8x dx x 1 e4x 8x dx

Use substitution to find the indefinite integral 92 z 9z 4dz

Use substitution to find the indefinite integral 5 5x 17 dx

Evaluate the following indefinite integral 1 7t5 2t 1 715 dt

Evaluate the following indefinite integral 3 x dx xdx Type an exact a

9 x 6x 3 3 x dx 9 6x 413 dx Type an exact ans

Evaluate 9x 9x 2 dx 9x 9x 2 dx Type an exact answer

14x 2ycbx Find the indefinite integral 14x 2 dx 14x Type an exact answer 2 dx

5 The graph of f x is shown below Use it to evaluate f x dx Area 7 1 2 4 5 Area 4 6

Use the Laws of Logarithms to evaluate the expression 1094 64 3

You can work with others or get help in the AAC 1 f x 4sin 2x 2 Period Phase shift Domain Reflected yes or no Scratch work Find the Amplitude Vertical shift Range I Overall shape S ref S cup ref cup

Use the integral table to find Sx e x dx x e3x e3x Ox xx c 3 O Xe3x 3 xe3x C e3x 9 Ox x3 0 x e3x e3x c a C C C

Evaluate using integration by parts S 5xex dx O 5ex 5xex C O xeX 5eX C O 5xex 5ex C 5ex ex C

2 sin x 3 sin 2x 1 In 1 1 2 2 1 21 In E dx is equal to In 2 sinx cosx 2 sinx cos x 2 sin x cos x 2 sinx cos x 2 sinx cos x 2 sinx cos x 3 4 none of these sin x cos x 3 2 tan 2 1 2V2 tan 1 2 2 2 tan sin x cos x 2 sin x cos x 1 2 c c c

9 93 Find f x if f x 3x Select one 3 O O X C 3 X 2 C 3 3 x 3 O x C

793 Find f x if f x 1 x Select one O O O O 2 In x 2 2 In x 2 1 C x In x C

1281 Evaluate sin 15 No GC 81 Select one O O O 2 6 4 6 2 4 6 2 2 6 2 4

5 3 Evaluate 2sinx dx Hint Just integrate sinx and add the 2 back on at the er 93 Select one cosx C 2cosx 2 cos x C 2cosx C

10 80 If f x cos x and g x Arccot x find f g 1 Select one 1 2 1 S S 2

The plot below represents the function f x 5 4 3 2 1 5 3 2 1 3 4 Evaluate f 1 f 1 1 3 4 5

Find the average rate of change of f x 8x 2 on the interval 5 a Your answer will be an expression involving a

1 2 Write the function as a sum of partial fractions Do not determine the numerical values of the coefficients 1 a 1 1 b 2 x x

3 20 Evaluate the integral 3 fx x cos 5x dx

1 2 Evaluate the integral using integration by parts with the indicated choices of u and dr 1 fx hxdx u lnx dr x dx

3 1 pt Verify the following 16 1 4x dx 8tan 2x C

37 ng Question 6 9465 Find an equation for the graph sketched bel 8 7 4 341 5 4 3 2 1 7 2 2 3 4 5 3 5 6 7 8 X 2 3 4 5

2 Given and Y x cos x Y2 x sin x satisfy the corresponding homogeneous equation of x y 2xy x 2 y x cos Find the general solution Y Yc Yp using variation of parameters

Find the volume of the following solid The tetrahedron bounded by the coordinate planes x 0 y 0 z 0 and the plane 5x 6y z 30 0 The volume is Simplify your answer Type an integer or a fraction www

Show that 4 is a lower bound and 2 is an upper bound for the real zeros of P x x 4 3x 3 4x 2 2x 7 Find all the zeros of the following polynomials

y sec x y tan x y cot x y csc x y cos x y sin x 4 HU B 2 1 1 3 2 1 1 2 A 3 4 5 6

nd the function f x if f x 2 12x12x and f 1 5 f 1 2

A retractable awning above a patio lowers at an angle of 50 from the exterior wall at a height of y 11 feet above the ground No direct sunlight is to enter the door when the angle of elevation of the sun is greater than 70 see figure What is the length x of the awning Round your answer to two decimal places X ft 70 Suns rays

a 5 points Use the trapezoidal rule with n 4 to find an approximation to the integral int 0 4 e 2 x d x You do not need to simplify your answer You will not receive credit for evaluating the integral b 5 points Using the error formula for the trapezoidal rule estimate how far your answer to a is from the actual value of the integral For full credit you should give and justify your estimate for M in the formula

Question 9 12 2 35 Part 4 of 4 The reduced row echelon form of a system of linear equations is given Write the system of whether the system is consistent or inconsistent If it is consistent give the solution What equation does the first row represent

Find the volume of the solid obtained by rotating the region enclosed by the graphs of y 21 x y 3x 7 and x 0 about the y axis v 0 V

blem 5 Find the volume of the solid that results when the red region is revolved about the x axis f x 5 x a 2 b 5 click on image to enlarge

Use the general slicing method to find the volume of the following solid The sold whose base is the region bounded by the semicircle y 196 2 and the x axis and whose cross sections through the solid perpendicular to the x axis are squares

Use the Integral test Limit Comparison test or Ratio tests to determine convergence or divergence of the following series a b k 1 8 k 1 C k 1 2k k 2 480 k 1 k 11

Find the area of the following region Sketch the bounding curves and the region in question The region bounded by y e y 18ex 3 and x 0 Sketch the bounding curves and the region in question Choose the correct answer below B B Q G O C Q G OD Set up the integral that will give the area of the region Use increasing limits of integration Select the correct choice below and fill in the answer boxes to complete your choice Type exact answers OA J Q

Vertical asymptotes at x 4 a x intercepts at x 1 and x 6 Horizontal asymptote at y 9 Question Help Video M Calculator

be the part of the plane 4x 1y z 2 which lies in the first octant oriented upward Use the Slokes theorem to find the flux of the vector field F 4i 4j 2k across the surface

6 Find all vertical and horizontal asymptotes of the function 3 x a x b 5 x a x c R x where a b and care distinct arbitrary constants In addition state all values of for which R is not continuous Sketch a possible graph of R clearly labeling the values of a b and c

4 5 marks Find a function y x satisfying dy dx y cos x 3 cos x y 0 5

Convert the angle 3T 4 from radians to degrees degrees

16 2 3591 16 22 16 2 SVO 1 16 23 23 2 y 22 1 2 dy dz dz