MAT 302 Assignment Problem 5.5

MAT 302 Assignment Problem 5.5 | Borough of Manhattan Community College

5.5 Integration By Substitution

Question 1

(1 point) Evaluate the integral by making the given substitution.

∫sec(6x)tan(6x)dx,u=6x

Question 2

(1 point) Evaluate the indefinite integral.

∫5sin2xcosxdx

Question 3

(1 point) Evaluate the indefinite integral.

∫x5(x6+5)3/2dx

Question 4

(1 point) Evaluate the indefinite integral.

∫(x2−2)3⋅2x1dx

Question 5

(1 point) Evaluate the indefinite integral.

∫12x33x4−10−−−−−−−√3dx∫12x33x4−103dx

Question 6

(1 point) Evaluate the indefinite integral.

∫x42+x5−−−−−√dx∫x42+x5dx

Question 7

(1 point) Evaluate the indefinite integral:

Question 8

(1 point) Evaluate the indefinite integral.

∫x5x3+1−−−−−√3dx∫x5x3+13dx

Question 9

(1 point)

Evaluate the integral

∫9x+1−−−−−√+x√dx

Question 10

(1 point) Note: You can get full credit for this problem by just answering the last question correctly. The initial questions are meant as hints towards the final answer and also allow you the opportunity to get partial credit.

Consider the definite integral ∫π/2π/6cos(z)sin9(z)dz∫π/6π/2cos⁡(z)sin9⁡(z)dz

Then the most appropriate substitution to simplify this integral is
uu = 

Then dz=f(z)dudz=f(z)du where
f(z)f(z) = 

After making the substitution and simplifying we obtain the integral ∫bag(u)du∫abg(u)du where
g(u)g(u) = 
aa = 
bb = 

Question 11

(1 point) Evaluate the definite integral:

Question 12

(1 point) Evaluate the definite integral

∫14301(3x−7)19dx

Question 13

(1 point) Evaluate

∫π√30x2cos(x3)dx.

Question 14

(1 point) Evaluate the definite integral.

∫π/20sin(2t)dt

Question 15

(1 point) Evaluate

∫32xx−2−−−−−√dx.

Question 16

(1 point) Evaluate

∫411x51+1x4−−−−−−√dx.∫141x51+1x4dx.

If the integral does not exist, enter DNE.

Question 17

(1 point) Use the odd/even function properties to evaluate the definite integral.

∫π2−π2sin2(x)cos(x)dx

Question 18

(1 point) Use the odd/even function properties to evaluate the definite integral.

∫5−5(x5+x3)x2+7−−−−−√dx

Question 19

(1 point) Use the odd/even function properties to evaluate the definite integral.

∫3−3xsin2(x)dx∫−33xsin2(x)dx

Question 20

(1 point) Evaluate the definite integral.

∫π2π3esin(7x)cos(7x)dx

Question 21

(1 point)

Evaluate the indefinite integral

∫5exex+1dx

Question 22

(1 point) Evaluate

∫20x3e−x4dx.

Question 23

1 point) Evaluate the definite integral:

∫20(e2x−2x)4(e2x−1)dx

Question 24

(1 point) Find the indefinite integral.

∫e7x+2e6x+4e5xe6xdx