In which of the following cases the value of the integral is more than 10? A. _0^2, x, dx B. _0^2 (x+3)^2 dx C. _0^2 e^x dx D. _0^2 (2x+5) dx Choose the correct answer from the options given below: Option 1: A and C only Option 2: C and D only Option 3: B and D only Option 4: A and D only

Answer: B and D only. Solution: _0^2, x, dx = 2 and _0^2 e^x dx = e^2-1 6.4, both below 10. But _0^2 (x+3)^2 dx = (125-27)/3 = 98/3 32.7 and _0^2 (2x+5)dx = 4+10 = 14 both exceed 10.

Calculus

Integrals

Medium

applied

In which of the following cases the value of the integral is more than 10?

A. $\displaystyle\int_0^2 |x|\,dx$

B. $\displaystyle\int_0^2 (x+3)^2\,dx$

C. $\displaystyle\int_0^2 e^x\,dx$

D. $\displaystyle\int_0^2 (2x+5)\,dx$

Choose the correct answer from the options given below:

A and C only

C and D only

B and D only

A and D only

✅ Correct Option: 3

$\int_0^2|x|dx = 2$ and $\int_0^2 e^x dx = e^2-1 \approx 6.4$ , both below $10$ . But $\int_0^2 (x+3)^2 dx = \frac{125-27}{3} = \frac{98}{3} \approx 32.7$ and $\int_0^2 (2x+5)dx = 4+10 = 14$ both exceed $10$ .

2025: 14 May Shift 1

Match List-I with List-II

List-I	List-II
Definite integral	Value
(A) $\int_0^1 \frac{2x}{1 + x^2} dx$	(I) 2
(B) $\int_{-1}^1 sin^3 x \cos^4 x dx$	(II) $log_e\left(\frac{3}{2}\right)$
(C) $\int_0^{\pi} \sin x dx$	(III) $log_e 2$
(D) $\int_2^3 \frac{2}{x^2 - 1} dx$	(IV) 0

Choose the correct answer from the options given below:

2022: 4 Aug Shift 1

$\int_{0}^{\pi} \frac{e^{\cos x}}{e^{\cos x} + e^{-\cos x}} dx =$

2026: 18 May Shift 1

Match List-I with List-II

List-I	List-II
(A) $\displaystyle\int_{\pi/6}^{\pi/3} \cos x \, dx$	(I) $0$
(B) $\displaystyle\int_{-\pi}^{\pi} (\sin^{61}x + x^{123}) \, dx$	(II) $4$
(C) $\displaystyle\int_{0}^{\pi/2} \dfrac{1}{1+\tan^3 x} \, dx$	(III) $\dfrac{\sqrt{3}-1}{2}$
(D) $\displaystyle\int_{-2}^{2} (2 - \left\vert x \right\vert) \, dx$	(IV) $\dfrac{\pi}{4}$

Choose the correct answer from the options given below:

2022: 4 Aug Shift 1

Match List I with List - II

List - I	List - II
A. An even function	I. $x^2 + \cos x$
B. For an even function, $\int_{-a}^{a} f(x)dx =$	II. 0
C. If $f(2a-x) = -f(x)$ , then $\int_{0}^{2a} f(x)dx =$	III. $2\int_{0}^{a} f(x)dx$
D. An odd function	IV. $x^3 + \sin x$

Choose the correct answer from the options given below:

2023: 22 May Shift 3

$\int_0^{\pi/2} \sqrt{1 - \sin 2x} \, dx$ is equal to :

2025: 14 May Shift 1

The integral I = $\int \frac{e^{5\log_e x} - e^{4\log_e x}}{e^{3\log_e x} - e^{2\log_e x}} dx$ is equal to

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