Question

By Trapezoidal rule, the value of ${\int }_0^1{x}^{3}dx$, considering five sub-intervals, is

• A. $0.20$
• B. $0.28$
• C. $0.27$
• D. $0.26$

Answer 1

The correct option is D $0.26$

Here, $h=\frac{1-0}{5}=0.2$
We have,
By Trapezoidal rule
${\int }_0^1{x}^{3}dx=\frac{0.2}{2}[(0+1)+2(0.008+0.064+0.216+0.512)]$
$=0.1[1+0.016+0.128+0.432+1.024]$
$=\frac{1}{10}\left[2.6\right]=0.26$