## anonymous 5 years ago Evaluate the integral with the aid of an appropriate u-sub: Integral sign { cos^19 (x)}^1/2 sinx dx

1. anonymous

tailor made for u-sub. put $u=cos(x)$ $du=-sin(x)dx$ $-\int u^{\frac{19}{2}}du$

2. anonymous

I see what I did wrong, I messed up the power. The whole cos^19 (x) messed me up. Thanks for your help, I appreciate it. : )

3. anonymous

You should get $-\int\limits_{}^{}\sin ^{1/2}{(u ^{19})} du$ From here you may have to jump into some trig identity im not sure

4. anonymous

actually there is no $sin^{\frac{1}{2}}$ in it. just take the anti derivative of $u^{\frac{9}{2}}$ which is $\frac{2}{11} u^{\frac{11}{9}}$ and then replace u by cos(x) don't forget the "-" sign in front like i did.

5. anonymous

oops i meant the antiderivative is $-\frac{2}{11}u^{\frac{11}{2}}$

6. anonymous

the problem they wrote there is $\int\limits_{}^{}\sin ^{1/2}[\cos ^{19}(x)]*\sin(x)*dx$