Let $f:\mathbf{R}\to\mathbf{R}$ be a function such that $f(x)+3f\left(\frac{\pi}{2}-x\right)=\sin x$, $x \in \mathbf{R}$. Let the maximum value of $f$ on $\mathbf{R}$ be $\alpha$. If the area of the region bounded by the curves $g(x)=x^2$ and $h(x)=\beta x^3$, $\beta>0$, is $\alpha^2$, then $30\beta^3$ is equal to __________.

JEE Main 2026 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 5 April 2026, Shift 2, Maths Q24

Question 24 of 75 in this shift, Maths question 24 of 25, Section B.

Let

f:\mathbf{R}\to\mathbf{R}

be a function such that

f(x)+3f\left(\frac{\pi}{2}-x\right)=\sin x

x \in \mathbf{R}

. Let the maximum value of

f

\mathbf{R}

\alpha

. If the area of the region bounded by the curves

g(x)=x^2

and

h(x)=\beta x^3

\beta>0

, is

\alpha^2

, then

30\beta^3

is equal to __________.

Official answer

NTA final key.

Chapter: Application of Integrals
Topic: Area Under Curves
Idea tested: Area Between Curves

Same idea in other shifts

Asked 22× in all

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6 Apr 2026, Shift 2 · Q19The area of the region $\{(x,y): x^2-8x\le y\le -x\}$ is :EasySingle correct
8 Apr 2026, Shift 2 · Q18Let $f : (1, \infty) \to \mathbf{R}$ be a function defined as $f(x) = \frac{x-1}{x+1}$ . Let $f^{i+1}(x) = f\left(f^{i}(x)\right)$ ,…HardSingle correct
7 Apr 2025, Shift 1 · Q19If the area of the region bounded by the curves $y = 4 - \frac{x^2}{4}$ and $y = \frac{x-4}{2}$ is equal to $\alpha$ , then $6\alpha$ equalsEasySingle correct
4 Apr 2024, Shift 1 · Q13One of the points of intersection of the curves $y=1+3x-2x^2$ and $y=\frac{1}{x}$ is $\left(\frac{1}{2}, 2\right)$ . Let the area of the…HardSingle correct
6 Apr 2024, Shift 1 · Q12Let the area of the region enclosed by the curves $y=3x$ , $2y=27-3x$ and $y=3x-x\sqrt{x}$ be $A$ . Then $10A$ is equal toMediumSingle correct
8 Apr 2024, Shift 2 · Q12The area of the region in the first quadrant inside the circle $x^2 + y^2 = 8$ and outside the parabola $y^2 = 2x$ is equal to :MediumSingle correct

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.