EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 26 - Definite Integration>WBJEE 2019>Q 11

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Let $I_{n} = \int_{0}^{1} x^{n} \tan^{- 1} x d x .$ If $a_{n} I_{n + 2} + b_{n} I_{n} = c_{n}$ for all $n \geq 1,$ then

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Important Questions on Definite Integration

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 26 - Definite Integration>WBJEE 2019>Q 12

The value of

\lim_{x \to 0} \frac{1}{x} [\int_{y}^{a} e^{\sin^{2} t} d t - \int_{x + y}^{a} e^{\sin^{2} t} d t]

is equal to

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 26 - Definite Integration>WBJEE 2018>Q 13

Let

I = \int_{π / 4}^{π / 3} \frac{\sin x}{x} d x .

Then

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 26 - Definite Integration>WBJEE 2018>Q 14

Let

I = \int_{0}^{1} \frac{x^{3} \cos 3 x}{2 + x^{2}} d x .

Then