Calculus

Integrals

Easy

applied

Match List-I with List-II

List-I List-II
(A) $\displaystyle\int_{-1}^{1}(2x^5+3x^3+4x+1)dx=$ (I) 2
(B) $\displaystyle\int_{-2}^{2}(4x^3+2)dx=$ (II) 12
(C) $\displaystyle\int_{-1}^{1}x^3dx=$ (III) 8
(D) $\displaystyle\int_{-3}^{3}(3x^5+2)dx=$ (IV) 0

Choose the correct answer from the options given below:

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

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

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

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

✅ Correct Option: 4

Odd powers integrate to zero over symmetric limits, leaving only the constant term.

(A) $\int_{-1}^{1}1\,dx = 2$

(B) $\int_{-2}^{2}2\,dx = 8$

(D) $\int_{-3}^{3}2\,dx = 12$

2025: 30 May Shift 1

$\int_0^{\pi/2} \frac{\sin^8 x}{\sin^8 x + \cos^8 x} dx$ is equal to

2026: 19 May Shift 1

The value of integral $I = \int_{3}^{5} \frac{x^2}{(x-1)(x-2)}\,dx$ is

2026: 29 May Shift 1

$\displaystyle\int_1^e x\log_ex\,dx$ is equal to:

2022: 23 Aug Shift 1

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:

2022: 10 Aug Shift 1

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

2022: 7 Aug Shift 2

If $f(x) = \begin{cases} 1 - 2x, & x \leq 0 \\ 1 + 2x, & x > 0 \end{cases}$ , then $\int_{-1}^{1} f(x) \, dx =$

Solution