evaluate integral

Question

definite integral sign a=1 b=8

4(x^(2/3)+14)^3/((x^(1/3))) dx

I get u= x^2/3 + 14
then du= 2/3 * x^(-1/3) dx
6 { u^4/4 | a=1 b=8

Then I get 3u^4/2 | a=1 b=8
2048-1.5= 2046.5

Is this correct. thank you all.

Answer 1

I did it wrong. The u= x^2/3 + 14

so my new calculation becomes 98304-75937.5= 22366.5

is that right? thanks

Answer 2

Your substitution for u is correct, so you wind up with

∫6u^3 du

Since u=x^2/3 + 14,
x=1 ==> u=15
x=8 ==> u=18
and you have

3u^4/2 [15,18]
= 157464 - 75937.5 = 81526.5

Not sure where you got 98304

Answer 3

I see what i did wrong. thanks!