Chapter 5.4, Problem 6CP

Use Adaptive Trapezoid Quadrature to approximate the definite integral within $0.5\times {10}^{-8}$.

1. ${\displaystyle {\int }_0^1{e}^{x^2}dx}$
2. ${\displaystyle {\int }_0^{\sqrt{\pi }}\sin x^{2}dx}$
3. ${\displaystyle {\int }_0^{\pi }{e}^{\cos x}dx}$
4. ${\displaystyle {\int }_0^1\text{In}\left(x^2+1\right)dx}$
5. ${\displaystyle {\int }_0^1\frac{xdx}{2e^x-e^{-x}}}$
6. ${\displaystyle {\int }_0^{\pi }\cos e^{x}dx}$
7. ${\displaystyle {\int }_0^1{x}^{x}dx}$
8. ${\displaystyle {\int }_0^{\pi /2}\text{In}\left(\cos x+\sin x\right)dx}$
9. .