# intergrate: cos theta sine^6 theta

• May 11th 2008, 07:49 PM
dangerous_dave
intergrate: cos theta sine^6 theta
Im still trying to wrap my head around the last one. But heres another im having trouble with : cos theta sine^6 theta
• May 11th 2008, 07:51 PM
Chris L T521
Quote:

Originally Posted by dangerous_dave
Im still trying to wrap my head around the last one. But heres another im having trouble with : cos theta sine^6 theta

Again, make a substitution $u=sin\theta \rightarrow du=cos\theta d\theta$. Substitute into the integral and you will now have:

$\int u^6 \,du$.

Integrate from here and substitute u back in and then you'll have your answer! Hope this helped you out! :D
• May 11th 2008, 07:53 PM
Mathstud28
Quote:

Originally Posted by dangerous_dave
Im still trying to wrap my head around the last one. But heres another im having trouble with : cos theta sine^6 theta

Alternatively $\int\cos(x)\sin^6(x)dx=\frac{1}{7}\int\bigg(\sin^7 (x)\bigg)'dx$
• May 11th 2008, 08:13 PM
dangerous_dave
Thank you :D