| utf35-002 Evaluate the following integrals, where $a$, $b$, and $c$ are constants, $a>0$. \begin{alignat*}{3} &a) \int{a^{bx}} & &b) \int{\frac{dx }{ bx+c}} & &c) \int{(bx+c)^n} \\ &d) \int{\frac{\ln {(ax)} }{ bx}} & &e) \int{\frac{dx }{ a^2+(bx)^2}} & &f) \int{\tan {(bx+c)}} \end{alignat*} |
| utf35-003 Prove that the area of the portion of the sphere shown below is $2\pi r h.$ {(Notice that this depends only on h, not on the position of the planes!)} |