问题及解答

$$I_c={\int }_0^1\frac{\cos x}{\sqrt{x}}\mathrm{d}x$$

$$I_s={\int }_0^1\frac{\sin x}{\sqrt{x}}\mathrm{d}x$$

使用梯形公式或辛普森公式进行近似计算.

(a)  Use the composite trapezoidal rule with $n$ intervals of $[0,1]$.  "ignoring" the singularity at $x=0$.

(b)  Use the composite trapezoidal rule over the interval $[h,1]$ where $h=1/n$ in combination with a weighted Newton-Cotes rule .