If the area of the region $\left\{(x, y): \left|4-x^2\right|\le y\le x^2,\ y\le4,\ x\ge0\right\}$ is $\left(\frac{80\sqrt{2}}{\alpha}-\beta\right)$, $\alpha, \beta\in\mathbf{N}$, then $\alpha+\beta$ is equal to ___________.

JEE Main 2025 · MathsNumerical answerNumerical valueHardCalculation

JEE Main 2 April 2025, Shift 1, Maths Q21

Question 21 of 75 in this shift, Maths question 21 of 25, Section B.

If the area of the region

\left\{(x, y): \left|4-x^2\right|\le y\le x^2,\ y\le4,\ x\ge0\right\}

\left(\frac{80\sqrt{2}}{\alpha}-\beta\right)

\alpha, \beta\in\mathbf{N}

, then

\alpha+\beta

is equal to ___________.

Official answer

NTA final key.

Chapter: Application of Integrals
Topic: Area Under Curves
Idea tested: Area with Modulus

Same topic in other shifts

All Area Under Curves questions

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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 42 of the 174 JEE Main shifts held from 2017 to 2026.