Page:Calculus Made Easy.pdf/248

 (4) Find $$\int x^2 \sin x\, dx$$.

Now find $$\int x \cos x\, dx$$, integrating by parts (as in Example 1 above):

Hence

(5) Find $$\int \sqrt{1-x^2}\, dx$$.

and $$x=v$$; so that

Here we may use a little dodge, for we can write

Adding these two last equations, we get rid of $$\int \dfrac{x^2\, dx}{\sqrt{1-x^2}}$$, and we have