Question

Prove that the integral from 0 to Infinity (sin^2(x)e^-x)dx converges using the comparison test.

Answer #1

A) Use the Comparison Test to determine whether integral from 2
to infinity x/ sqrt(x^3 -1)dx is convergent or divergent.
B)Use the Comparison Test to determine whether the integral from
2 to infinity (x^2+x+2)/(x^4+x^2-1) dx is convergent or
divergent.

Determine whether the improper integral from 5 to infinity
3/square root x dx converges or diverges, and find the value if it
converges.
Select the correct choice below and fill in any answer boxes
within your choice.
A. The value of the integral
B.The integral diverges.

definite integral 0 to 7 of e^(x)sin(x)dx

Explain whether the following integrals converge or not. If the
integral converges, find the value. If the integral does not
converge, describe why (does it go to +infinity, -infinity,
oscillate, ?)
i) Integral from x=1 to x=infinity of x^-1.4 dx
ii) Integral from x=1 to x=infinity of 1/x^2 * (sin x)^2 dx
iii) Integral from x=0 to x=1 of 1/(1-x) dx

Determine the convergence or divergence if each integral by
using a comparison function. Show work using the steps below:
A. Indicate the comparison function you are using.
B. Indicate if your comparison function is larger or smaller
than the original function.
C. Indicate if your comparison integral converges or diverges.
Explain why.
D. State if the original integral converges or diverges. If it
converges, you don’t need to give the value it converges to.
11. integral from 1 to infinity...

Integrate -infinity to -3 x/(x^2+x-2)dx if it
converges

1. Integral sin(x+1)sin(2x)dx
2.Integral xe^x dx
3. integral ln sqrt(x) dx
4. integral sqrt(x) lnx dx

to calculate the integral from (-infinty) to (+ infinity) of
[x^2 / (x^4 + 4)[ dx . poles, different
residues.

using reduction formula***
13. Evaluate, ∫ sin 5x cos x dx. Also prove that, ∫ sin mx cos
nx dx = 0

1a) Evaluate the limit as x goes to infinity using l'hopitals
rule
(x^-1/3)/sin(1/x)
1b) Evaluate the improper integral (if convergent find it's
value)
(secx-tanx)dx where a= 0 and b=pi/2

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