Chapter 5.4, Problem 1CP

Use Adaptive Trapezoid Quadrature to approximate the definite integral within $0.5\times {10}^{-8}$ . Report the answer with eight correct decimal places and the number of subintervals required.

1. ${\displaystyle {\int }_0^4\frac{xdx}{\sqrt{x^2+9}}}$
2. ${\displaystyle {\int }_0^1\frac{x^{3}dx}{x^2+1}}$
3. ${\displaystyle {\int }_0^{1}x{e}^{x}dx}$
4. ${\displaystyle {\int }_1^3{x}^2\text{In}xdx}$
5. ${\displaystyle {\int }_0^{\pi }{x}^2\sin xdx}$
6. ${\displaystyle {\int }_2^3\frac{x^{3}dx}{\sqrt{x^4-1}}}$
7. ${\displaystyle {\int }_0^{2\sqrt{3}}\frac{dx}{\sqrt{x^2+4}}dx}$
8. ${\displaystyle {\int }_0^1\frac{xdx}{\sqrt{x^4+1}}dx}$
9. .