Saturday 24 October 2015

calculus - Evaluate $int_{0}^{pi}sin^5{theta}cos^2{theta} dtheta$

I'm trying to find the mass of a spherical object with a given density function, and to do so I must solve this integral $$\int_{0}^{\pi}\sin^5{\theta}\cos^2{\theta}\ d\theta,$$



but no matter which method I choose (integration by parts, substitution, etc) I can't for the life of my figure out the anti-derivative.

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real analysis - How to find $lim_{hrightarrow 0}frac{sin(ha)}{h}$

How to find $\lim_{h\rightarrow 0}\frac{\sin(ha)}{h}$ without lhopital rule? I know when I use lhopital I easy get $$ \lim_{h\rightarrow 0}...