PROBLEMS, SECTION 7
Express the following integrals as B functions, and then, by (7.1), in terms of I functions.
When possible, use I function formulas to write an exact answer in terms of π, √2, etc.
Compare your answers with computer results and reconcile any discrepancies.
1. $\int_0^1 \frac{x^4}{\sqrt{1-x^2}} dx$
2. $\int_0^{\pi/2} \sqrt{\sin^3 x \cos x} dx$
3. $\int_0^1 \frac{dx}{\sqrt{1-x^3}}$