Question

U-substitution for definite integrals. Can someone please check where I went wrong - answer supposed to be 3...

Answer 1

\[\int\limits_{0}^{13}\frac{ dx }{ \sqrt[3]{(1+2x)^2} }\]
\[u=1+2x\] \[du=2dx\]
changing limits of integration I get
\[\frac{ 1 }{ 2 } \int\limits_{1}^{27}u^\frac{ -2 }{ 3 }du\]
\[=\frac{ 1 }{ 2 }(-3u^\frac{ -1 }{ 3 } )\]
\[(-\frac{ 3 }{ 2\sqrt[3]{27} }+\frac{ 3 }{ 2\sqrt[3]{1} })=-\frac{ 1 }{ 2 }+\frac{ 3 }{ 2 }=1\]

Answer 2

should n't your penultimate line be

1/2(3 u ^ (1/3) ?

Answer 3

When you were integrating u^-2/3, it should be 3u^1/3, not 3u^-1/3

Answer 4

yep that's it

Answer 5

I see it, thanks!

Answer 6

Yep.