If _0^a 3x^2dx = 8, then the value of a is: Option 1: 2 Option 2: 10 Option 3: 8 Option 4: 5

Answer: 2. Solution: Given _0^a 3x^2dx = 8 The antiderivative of 3x^2 is: 3x^2 dx = 3 * x^3/3 = x^3 Applying the limits from 0 to a: [x^3]_0^a = a^3 - 0^3 = a^3 From the given information: a^3 = 8 a = 3√8 a = 2 Therefore, the value of a is 2.

Calculus

Integrals

Easy

core

If $\int_0^a 3x^2dx = 8$ , then the value of $a$ is:

✅ Correct Option: 1

Given $\int_0^a 3x^2dx = 8$

The antiderivative of $3x^2$ is:

$\int 3x^2 dx = 3 \cdot \frac{x^{3}}{3}$

$= x^3$

Applying the limits from 0 to $a$ :

$\left[x^3\right]_0^a = a^3 - 0^3$

$= a^3$

From the given information:

$a^3 = 8$

$a = \sqrt[3]{8}$

$a = 2$

Therefore, the value of $a$ is $2$ .

2025: 22 May Shift 2

Match List-I with List-II (where $c$ is an arbitrary constant)

List-I	List-II
(A) $\int \tan x \, dx$	(I) $\log\vert \sec x + \tan x\vert + c$
(B) $\int \cot x \, dx$	(II) $\log\vert \sec x\vert + c$
(C) $\int \sec x \, dx$	(III) $\log\vert \sin x\vert + c$
(D) $\int \cosec x \, dx$	(IV) $\log\vert \cosec x - \cot x\vert + c$

Choose the correct answer from the options given below:

2025: 14 May Shift 1

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2022: 25 May Shift 1

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

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$\int \frac{\sqrt{\tan x}}{\sin x \cos x} dx$ equals :

2022: 7 Aug Shift 2

$\int_{0}^{1} x^2 e^{x^3} \, dx$ is equal to :

2025: 22 May Shift 2

$\int_0^2 (|x| + |x - 2|) dx =$

If ∫0a3x2dx=8\int_0^a 3x^2dx = 8∫0a​3x2dx=8, then the value of aaa is:

Solution

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If $\int_0^a 3x^2dx = 8$ , then the value of $a$ is: