Chapter 5, Problem 29RE

In each part, evaluate the integral. Where appropriate, you may use a geometric formula.

(a) ${\displaystyle {\int }_{-1}^1\left(1+\sqrt{1-x^2}\right)dx}$

(b) ${\displaystyle {\int }_0^3\left(x\sqrt{x^2+1}-\sqrt{9-x^2}\right)dx}$

(c) ${\displaystyle {\int }_0^{1}x\sqrt{1-x^4}dx}$