MATH 101 Webwork 5 Homework Questions and Answers PDF from 2020

Nikita Sharma 2019W2 MATH 101 209
Assignment Homework 5 due 9/12/14 at 9pm




1. (1 point) 6. (1 point) Use integration by parts to evaluate the indefinite
Evaluate the indefinite integral. integral Z
4x sin(x) dx.
ln x
Z
dx Answer:
x4
Correct Answers:
• 4*[-x*cos(x)+sin(x)]+C
Answer = +C 7. (1 point) Evaluate the following integral
Correct Answers: Z
2
• -x**(1-4)*ln(x)/(4-1) - x**(1-4)/(4-1)**2 ye2y dy.

Answer:
2. (1 point) Use integration by parts to evaluate the integral. Correct Answers:
Z • 0.25*eˆ(2*yˆ2)+C
216x2 cos(6x)dx
8. (1 point) First make a substitution and then use integration
by parts to evaluate the integral
Z
√

+C 3 sin x dx.
Correct Answers:
Answer:
• 216*(1/6*xˆ2*sin(6*x)+2*(1/6)**2*x*cos(6 * x)-2*(1/6)**3*sin(6*x))
Correct Answers:
• 6*[sin(sqrt(x))-sqrt(x)*cos(sqrt(x))]+C
Z 3. (1 point) Use integration by parts to evaluate the integral.
9. (1 point) Use integration by parts to evaluate the definite
(ln(5x))2 dx = +C
integral
Correct Answers: Z 3
te−t dt.
• x*(ln(5*x))ˆ2 - 2*x*ln(5 *x) + 2*x 0
Answer:
4. (1 point) Correct Answers:
Evaluate the indefinite integral. Remember that every indef- • -3*eˆ(-3)-eˆ(-3)+1
inite integral must include an additive constant, which you can
10. (1 point) Use integration by parts to evaluate the definite
enter as + C.
integral
Z 12
ln(x8 ) dx.
Z
x arctan(4x)dx 3
Answer:
Correct Answers:
Answer:
• 8*12*ln(12)-8*12-[8*3*ln(3)-8*3]
Correct Answers: 11. (1 point) Evaluate the definite integral.
• (1+16*xˆ2)/32*atan(4*x)-x/8+C
Z 8
t 3 ln(5t)dt
5. (1 point)
R
4
Evaluate x cos(182x)dx. Use capital C for your constant of in-
tegration.

Correct Answers:
Correct Answers:
• x*sin(182*x)/182 + cos(182*x)/(182*182) + C
• (8ˆ(4)/4)*(ln(5*8) - 1/4) - (4ˆ(4)/4)*(ln(5*4) - 1/4)

1