JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Analyzing +4 | -1

Let

J=\int\limits_{0}^1 \frac{\cos x}{\sqrt{x}} d x

and

K=\int\limits_{0}^1 \frac{\sin x}{\sqrt{x}} \mathrm{dx}

. Then which one of the following is true?

View answer and explanation

Correct option: A

\mathrm{K}<2 / 3

and

\mathrm{J}<2

Option A (K < 2/3 and J < 2) is correct because by comparing the integrands with simpler functions, we can establish the inequalities for the integrals.

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