Question

By trapezoidal rule the value of the integral $\int_{1}^{5}{x^{2}dx}$ on dividing the interval into four equal parts is

• A. 42
• B. 41.3
• C. 41
• D. 40

Answer 1

Answer: (A)

42

Answer 2

$h = \frac{5 - 1}{4} = 1$

x :	1	2	3	4	5
y :	1	4	9	16	25

$\int_{1}^{5}{x^{2}dx} = \frac{h}{2}\left\lbrack (y_{0} + y_{4}) + 2(y_{1} + y_{2} + y_{3}) \right\rbrack = \frac{1}{2}\left\lbrack (1 + 25) + 2(4 + 9 + 16) \right\rbrack = \frac{1}{2}\lbrack 26 + 58\rbrack = \frac{84}{2} = 42$