Question

Using trapezoidal method find ${\int }_0^3{e}^{x^2}$dx with step size h = 0.5

• A. 2319.07

Answer 1

The correct option is A 2319.07
Let
So,

x	0	0.5	1	1.5	2	2.5	3
y	1 = $y_0$	1.284 = $y_1$	2.718 = $y_2$	9.488 = $y_3$	54.598 = $y_4$	518.01 = $y_5$	8103.084 = $y_6$

Now using trapezoidal method,

${\int }_0^3{e}^{x^2}dx=\frac{0.5}{2}\left[\right(y_0+y_6)+2(y_1+y_2+y_3+y_4+y_5\left)\right]$
$=\frac{0.5}{2}[8104.084+2[586.098\left]\right]$
$=\frac{0.5}{2}\left[9276.28\right]$
= 2319.07