Question

Assertion($A$): lf $e=2.72,e^2=7.39$,$e^3=20.09,e^4=54.6$ then ${\int }_0^4{e}^{x}dx$ by Simpson's rule is $53.873$
Reason(R): Simpson's rule is ${\int }_a^{b}ydx=\frac{h}{2}$ $\left[\right(y_0+y_n)+2(y_1+y_2+\dots ..+y_{n-1}\left)\right]$

• A. Both A and R are true and R is the correct explanation of A.
• B. Both A and R are true but R is not the correct explanation of A.
• C. A is true but R is false.
• D. A is false but R is true.

Answer 1

Answer: (C)

A is true but R is false.

$A$ $e=2.72,e^2=7.39$,$e^3=20.09,e^4=54.6$
${\int }_0^4{e}^{x}dx$
${\int }_a^{b}f\left(x\right)dx=\frac{b-a}{3}\left[f\right(x_0)+4f(x_1)+2f(x_2)+f(x_3)+4f(x_4\left)\right]$
$=\frac{4}{3}[1+4(2.72)+2(7.39)+(20.09)+4(54.6\left)\right]$
$=53.873squnits$
R is false