Please help me with calculus .. Having serious problems!

(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.)

(answer from B)http://webwork.nuigalway.ie/webwork2...0c41fac051.png(answer from A) =?

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

Re: Please help me with calculus .. Having serious problems!

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.)

(answer from B)http://webwork.nuigalway.ie/webwork2...0c41fac051.png(answer from A) =?

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

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

C: if$\displaystyle w=x^3+1$ then $\displaystyle dw=3x^2dx$. Can you take it from here

Re: Please help me with calculus .. Having serious problems!

I think you mean to compare the answers from (B) and (D), which should differ only by a constant. After all, there is only one integral of that function, right?

Are you having trouble with the calculations in (A) through (D)? If so, tell us where you're having trouble.

- Hollywood