Substitution in Definite Integrals

[mattflint50]

Ok, I was doing my Calc homework and I was easily able to figure out every other substitution in Definite Integrals problem except this one.

7.) Evaluate the Integral from radical 7 to 0. The integral of x(x^2+1)^(1/3)dx
To integrate this a let u=x^+1, meaning the du=2xdx, making the above intergral= 1/2 (u)^(1/3)du. I integrated this making it 1/2 (u)^1(1/3) divided by 1 (1/3). SO I then plugged in radical 7. making it 1/2 (radical 7)^1(1/3) divided by 1(1/3), and I subtracted what I got when I plugged in 0. 0^1(1/3) divided by 1(1/3).
As an end result I got radical 7^1(1/3) divided by 2 (2/3)

This answer isnt even close to being right, given that my book says the answer is 45/8. Can you please help me!!!!!!!!!!!!!!!!!!!!!!!!!!

 

[royhaas]

When you make a change of variable you must also change the limits of integration. You didn't do that. The book answer is correct.

The alternative is to back-substitute and use the original limits.