• Feb 24th 2013, 10:18 AM
THKelly
(Crying)
Consider the integral 8x^2 (x^3+1) dx . In the following, we will evaluate the integral using two methods.
A:
First, rewrite the integral by multiplying out the integrand:
=?
B:
Then evaluate the resulting integral term-by-term:
=?
C:
Next, rewrite the integral using the substitution w=x^3+1
=?
D:
Evaluate this integral (and back-substitute for http://webwork.nuigalway.ie/webwork2...9b8ccd6cf1.png) to find the value of the original integral:
=?
E:
How are your expressions from parts (A) and (B) different? What is the difference between the two? (Ignore the constant of integration.)

Any help with this would be much appreciated!
(Happy)
• Feb 24th 2013, 10:38 AM
BobSacamano
Quote:

Originally Posted by THKelly
(Crying)
Consider the integral 8x^2 (x^3+1) dx . In the following, we will evaluate the integral using two methods.
A:
First, rewrite the integral by multiplying out the integrand:
=?
B:
Then evaluate the resulting integral term-by-term:
=?
C:
Next, rewrite the integral using the substitution w=x^3+1
=?
D:
Evaluate this integral (and back-substitute for http://webwork.nuigalway.ie/webwork2...9b8ccd6cf1.png) to find the value of the original integral:
=?
E:
How are your expressions from parts (A) and (B) different? What is the difference between the two? (Ignore the constant of integration.)

Any help with this would be much appreciated!
(Happy)

A/B: $\int (8x^5+8x^2) dx$ can you integrate this term by term?

C: if $w=x^3+1$ then $dw=3x^2dx$. Can you take it from here
• Feb 24th 2013, 03:58 PM
hollywood