The integral $\mathop \smallint \limits_{{x_1}}^{{x_2}} {x^2}dx$ 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?

Question

The integral $\mathop \smallint \limits_{{x_1}}^{{x_2}} {x^2}dx$ 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?

TuteeHUB · Accepted Answer

J < I

TuteeHUB · Answer

J > I

TuteeHUB · Answer

J = I

TuteeHUB · Answer

Insufficient data to determine the relationship

1.	The integral \(\mathop \smallint \limits_{{x_1}}^{{x_2}} {x^2}dx\) 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 > I
B.	J < I
C.	J = I
D.	Insufficient data to determine the relationship
Answer» B. J < I

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