CUET Mathematics - Calculus - Integrals | Free Questions - Page 11

Q1:

2022: 23 Aug Shift 1

Calculus

>

Integrals

Easy

Core

$\int \frac{dx}{\sin^2 x \cos^2 x} =$

$\tan x + \cot x + C$

$\tan x - \cot x + C$

$\tan x \cot x + C$

$\tan x - \cot 2x + C$

Correct Answer

Option 2

Correct Answer

Explanation

Q2:

2022: 23 Aug Shift 1

Calculus

>

Integrals

Medium

Core

$\int \sqrt{x^2 - 4x + 5} \, dx =$

$\left(\frac{x-2}{2}\right)\sqrt{x^2 - 4x + 5} + \log\left|(x-2) + \sqrt{x^2 - 4x + 5}\right| + C$

$\left(\frac{x-2}{2}\right)\sqrt{x^2 - 4x + 5} + \frac{1}{2}\log\left|(x-2) + \sqrt{x^2 - 4x + 5}\right| + C$

$\left(\frac{x-2}{2}\right)\sqrt{x^2 - 4x + 5} + \frac{1}{4}\log\left|(x-2) + \sqrt{x^2 - 4x + 5}\right| + C$

$\left(\frac{x-2}{2}\right)\sqrt{x^2 - 4x + 5} + \frac{3}{4}\log\left|(x-2) + \sqrt{x^2 - 4x + 5}\right| + C$

Correct Answer

Option 2

Correct Answer

Explanation

Q3:

2022: 23 Aug Shift 1

Calculus

>

Integrals

Easy

Core

Match List I with List II

List - I	List - II
A. $\int \frac{dx}{x^2 - a^2} =$	I. $\log_e\left\lvert x + \sqrt{x^2 + a^2}\right\rvert + C$
B. $\int \frac{dx}{a^2 - x^2} =$	II. $\frac{1}{2a}\log_e\left\lvert\frac{x-a}{x+a}\right\rvert + C$
C. $\int \frac{dx}{\sqrt{x^2 - a^2}} =$	III. $\frac{1}{2a}\log_e\left\lvert\frac{a+x}{a-x}\right\rvert + C$
D. $\int \frac{dx}{\sqrt{x^2 + a^2}} =$	IV. $\log_e\left\lvert x + \sqrt{x^2 - a^2}\right\rvert + C$

Choose the correct answer from the options given below:

A-II, B-III, C-IV, D-I

A-I, B-III, C-IV, D-II

A-II, B-IV, C-I, C-III

A-IV, B-III, C-II, D-I

Correct Answer

Option 1

Correct Answer

Explanation

Q4:

2022: 25 May Shift 1

Calculus

>

Integrals

Easy

Common

$\int_{0}^{1.5} [x] dx$ , where $[x]$ denotes the greatest integer function $\leq x$ , is equal to :

$\frac{1}{4}$

$\frac{1}{2}$

$1$

$0$

Correct Answer

Option 2

Correct Answer

Explanation

Q5:

2022: 25 May Shift 1

Calculus

>

Integrals

Hard

Core

$\int \left(\frac{1+x+x^2}{1+x^2}\right) e^{\tan^{-1} x} dx =$

$x + e^{\tan^{-1} x} + c$

$e^{\tan^{-1} x} - x + c$

$e^{\tan^{-1} x} + c$

$x e^{\tan^{-1} x} + c$

Correct Answer

Option 4

Correct Answer

Explanation

Q6:

2022: 25 May Shift 1

Calculus

>

Integrals

Hard

Core

Match List I with List II

LIST I	LIST II
A. $\int \frac{\sin x}{1 + \cos x} \, dx$	I. $e^{\tan^{-1} x} + C$
B. $\int \frac{1}{1 - \tan x} \, dx$	II. $\log(\log x + 1) + C$
C. $\int \frac{e^{\tan^{-1} x}}{1 + x^2} \, dx$	III. $-\log\lvert 1+\cos x \rvert + C$
D. $\int \frac{1}{x + x \log x} \, dx$	IV. $\frac{x}{2} - \frac{1}{2}\log\lvert \cos x - \sin x \rvert + C$

Choose the correct answer from the options given below:

A-II, B-III, C-IV, D-I

A-III, B-IV, C-I, D-II

A-I, B-II, C-III, D-IV

A-IV, B-I, C-III, D-II

Correct Answer

Option 2

Correct Answer

Explanation

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