Calculus

Integrals

Easy

common

Match the LIST-I with LIST-II

LIST-I (Definite integral) LIST-II (Value of definite integral)
A. $\displaystyle\int_4^9 \dfrac{1}{\sqrt{x}}\,dx$ I. $\dfrac{2}{3}$
B. $\displaystyle\int_{-1}^1 x^3\,dx$ II. 1
C. $\displaystyle\int_{-1}^1 x^2\,dx$ III. 0
D. $\displaystyle\int_1^2 [x]\,dx$ , where $[\cdot]$ denotes greatest integer function IV. 2

Choose the correct answer from the options given below:

LIST-I (Definite integral)		LIST-II (Value of definite integral)
A. $\displaystyle\int_4^9 \dfrac{1}{\sqrt{x}}\,dx$		I. $\dfrac{2}{3}$
B. $\displaystyle\int_{-1}^1 x^3\,dx$		II. 1
C. $\displaystyle\int_{-1}^1 x^2\,dx$		III. 0
D. $\displaystyle\int_1^2 [x]\,dx$ , where $[\cdot]$ denotes greatest integer function		IV. 2

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

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

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

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

✅ Correct Option: 3

A: $\int_4^9 x^{-1/2}dx = 2\sqrt{x}\big|_4^9 = 6-4 = 2$ (IV).

B: $x^3$ is odd on a symmetric interval, so the value is $0$ (III).

C: $\int_{-1}^1 x^2 dx = 2/3$ (I).

D: on $(1,2)$ , $[x]=1$ , so the integral is $1$ (II).

2026: 21 May Shift 2

Match the LIST-I with LIST-II

	LIST-I Definite Integrals		LIST-II Values
A.	$\displaystyle\int_{-1}^{1} \vert x \vert \, dx$	I.	$2$
B.	$\displaystyle\int_{-1}^{1} \sin^3 x \cos^4 x \, dx$	II.	$1$
C.	$\displaystyle\int_{-1}^{1} 3\vert x \vert^2 \, dx$	III.	$0$
D.	$\displaystyle\int_{0}^{4} \vert x-1 \vert \, dx$	IV.	$5$

Choose the correct answer from the options given below:

2022: 23 Aug Shift 1

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

2026: 15 May Shift 1

If '[.]' is greatest integer function, then value of $\displaystyle\int_0^{1.5}[x^2]\,dx$ is equal to :

2026: 30 May Shift 2

Match List-I with List-II

Choose the correct answer from the options given below:

2026: 21 May Shift 2

$\displaystyle\int e^x(\sec x + \log_e(\sec x + \tan x))dx$ is equal to: (where C is an arbitrary constant)

2025: 14 May Shift 2

The value of the definite integral $I = \int_{1}^{2} \frac{1}{x(1 + x^2)}dx$ is:

Solution