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JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Understanding +4 | -1

If

I=\int\limits_{0}^{\pi / 4} \sin ^2 x d x

and

J=\int\limits_{0}^{\pi / 4} \cos ^2 x d x

, then

I=

View answer and explanation

Correct option: A

\frac{\pi}{4}-J

Option C is correct because the integrals of sin²(x) and cos²(x) from 0 to π/4 are related by I + J = π/4.

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[*]

denotes the greatest integer function, is The integral

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is equal to: The definite integral

\int\limits_{{-2}}^0\left(x^3+3 x^2+3 x+3+(x+1) \cos (x+1)\right) d x

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I\,\,\left( {m + 1,\,\,n + 1} \right)