The integral $\int_{x_{1}}^{x_{2}} x^{2} d x$ with $x_{2}>x_{1}>0$ is evaluated analytically as well as numerically using a single application of the trapezoidal rule. If $I$ is the exact value of the integral obtained analytically and $J$ is the approximate value obtained using the trapezoidal rule, which of the following statements is correct about their relationship?

(A) $J>1$

(B) $J<1$

(C) $J=I$

(D) Insufficient data to determine the relationship

The integral $\int_{x_{1}}^{x_{2}} x^{2} d x$ with $x_{2}>x_{1}>0$ is evaluated analytically as well as numerically using a single application of the trapezoidal rule. If $I$ is the exact value of the integral obtained analytically and $J$ is the approximate value obtained using the trapezoidal rule, which of the following statements is correct about their relationship?

(A) $J>1$

(B) $J<1$

(C) $J=I$

(D) Insufficient data to determine the relationship

1 Answer - 5876 Votes