JEE Main 2026 · 2 Apr · Shift 1 · Mathematics Q25

MathematicsInteger+4 / -1Question 25 of 75

If $\alpha=\displaystyle\int_0^{2\sqrt3}\log_2\left(x^2+4\right)dx+\int_2^4\sqrt{2^x-4}\,dx$ , then $\alpha^2$ is equal to ________.

Your answer

Answer and worked solution

Official answer: 192

Inverse functions. $f(x)=\log_2(x^2+4)$ increases on $[0,2\sqrt3]$ from 2 to 4, and its inverse is $f^{-1}(y)=\sqrt{2^y-4}$ on $[2,4]$ .

Area identity.
$\int_0^{2\sqrt3}f+\int_2^4f^{-1}=2\sqrt3\cdot f(2\sqrt3)-0\cdot f(0)=8\sqrt3.$

Value. $\alpha^2=192$ .

Answer: 192

JEE Main 2026 · 2 Apr · Shift 1, Mathematics question 25