Mathematics · JEE

Hard Evaluation of definite integrals MCQs for JEE

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Hard Evaluation of definite integrals MCQs train multi-concept problem solving — attempt after mastering easy and medium sets (6+ on Goodmarks).

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Syllabus context

Part of Integral Calculus in JEE Main Mathematics.

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Q1MathsUnit 8: Integral Calculus

Evaluate:

\int_{1}^{2} \log x d x

Q2MathsUnit 8: Integral Calculus

I_{n}=\int_{0}^{\pi / 4} \tan ^{n} x d x,

then

\frac{1}{I_{2}+I_{4}}, \frac{1}{I_{3}+I_{5}}, \frac{1}{I_{4}+I_{6}}, \dots

are in

Q3MathsUnit 8: Integral Calculus

\boldsymbol{n} \stackrel{L t}{\rightarrow} \infty\left[\frac{\boldsymbol{n}+\mathbf{1}}{\boldsymbol{n}^{2}+\mathbf{1}^{2}}+\frac{\boldsymbol{n}+\boldsymbol{2}}{\boldsymbol{n}^{2}+\mathbf{2}^{2}}+\ldots+\right.

\left.\frac{\boldsymbol{n}+\boldsymbol{n}}{\boldsymbol{n}^{2}+\boldsymbol{n}^{2}}\right]=

Q4MathsUnit 8: Integral Calculus

Evaluate the following as the limit of sum :

\int_{0}^{2}(x+4) d x

Q5MathsUnit 8: Integral Calculus

\boldsymbol{I}_{n}=\int_{0}^{\frac{\pi}{4}} \tan ^{n} x d x

then

\frac{1}{I_{2}+I_{4}}, \frac{1}{I_{3}+I_{5}}, \frac{1}{I_{4}+I_{6}}

are in?

Q6MathsUnit 8: Integral Calculus

\int_{100}^{2014} \frac{\sqrt{x}}{\sqrt{2114-x}+\sqrt{x}} d x=

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