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 ) 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)(answer from A) =?
Any help with this would be much appreciated!
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.