JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

If a function

f:[0,27] \rightarrow \mathbf{R}

is differentiable then for some

0<\alpha<\beta<3, \int\limits_{0}^{27} f(x) \mathrm{d} x

is equal to

View answer and explanation

Correct option: C

3\left[\alpha^2 f\left(\alpha^3\right)+\frac{1}{2} \beta^2 f\left(\beta^3\right)\right]

Option C is correct because it correctly applies the Mean Value Theorem for integrals and derivatives to the given function and interval.

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