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JEE • MATHEMATICS • DEFINITE INTEGRATION

Definite integration practice · Mixed difficulty

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Practice format and chapter quiz

These sets use single-correct-answer MCQs. They do not cover every JEE Main or JEE Advanced question format and are not full-length mock papers.

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991 Easy

991 of 995

Application +4 | -1

The value

I=\int\limits_{0}^{\pi / 2} \frac{1}{1+\cot x} d x

View answer and explanation

Correct option: C

\pi / 4

Option C (

\pi/4

) is correct because using the property

\int_0^a f(x) dx = \int_0^a f(a-x) dx

simplifies the integral to

\pi/4

992 Easy

992 of 995

Application +4 | -1

\int \limits_0^\infty \,{e^{ - {x^2}}}\,\,dx = \sqrt {\frac{\pi }{2}}

then

\int \limits_0^\infty \,\,{e^{ - a{x^2}}}\,\,dx,\,\,\;a > 0

View answer and explanation

Correct option: D

\frac{1}{2}\,\,\frac{{\sqrt \pi }}{a}

Option D (

\frac{1}{2}\,\frac{{\sqrt {\pi } }}{a}

) is correct because it follows from a u-substitution and the given integral value.

993 Easy

993 of 995

Application +4 | -1

\lim\limits_{n \to \infty } \,\,\left\{ {\frac{1}{{na}}\,\, + \,\,\frac{1}{{na + 1}}\,\, + \,\,\frac{1}{{na + 2}}\,\, + \,\, \ldots + \,\,\frac{1}{{nb}}} \right\}

is equal to

View answer and explanation

Correct option: A

\log \,\,\left( {\frac{b}{a}} \right)

Option A (

\log \,\,\left( {\frac{b}{a}} \right)

) is correct because the limit of the Riemann sum is correctly converted to a definite integral and evaluated.

994 Medium

994 of 995

Analyzing +4 | -1

\phi \left( x \right) = \cos \,\,\,x\, - \int \nolimits_0^x \,\,\left( {x - t} \right)\,\,\phi \,\,\left( t \right)\,\,dt

, then

\phi ''\,\,\left( x \right)\,\, + \,\,\phi \,\,\left( x \right)

is equal to

View answer and explanation

Correct option: A

- \,\,\cos \,\,x

Option A is correct because after differentiating the given equation twice and simplifying,

\phi ''\,\,\left( x \right)\,\,+ \,\,\phi \,\,\left( x \right)

is equal to

- \,\,\cos \,\,x

995 Medium

995 of 995

Application +4 | -1

\int \frac{\sin x}{\sin (x-\alpha)} d x=A x+B \log \sin (x-\alpha),+C

, then value of

(A, B)

View answer and explanation

Correct option: B

(\cos \alpha, \sin \alpha)

Option B (

\cos \alpha, \sin \alpha

) is correct because after expanding and integrating, the coefficients of x and the logarithm term match these values.

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Review DEFINITE INTEGRATION in your textbook or class notes, then use this set to check your understanding.

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Definite integration practice · Mixed difficulty

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