Mathematics · 2026
JEE Main · 2 April 2026, Shift 1 · Q25
If α=∫_0^2 √ 3 log_2(x^2+4) d x+∫_2^4 √(2^x-4) d x, then α^2 is equal to ____.
If $\displaystyle \alpha=\int_0^{2 \sqrt{3}} \log _2\left(x^2+4\right) \mathrm{d} x+\int_2^4 \sqrt{2^x-4} \mathrm{~d} x$, then $\displaystyle \alpha^2$ is equal to $\displaystyle \_\_\_\_$.
Official answer
From NTA’s final answer key for this paper.
192
More from Definite Integration
- The value of the integral ∫_0^2 (√(x(x^2+x+1)))/((√(x+1))(√(x^4+x^2+1))) d x is equal to:2026
- The value of the integral ∫_-1^1((x^3+|x|+1)/(x^2+2|x|+1)) d x is equal to:2026
- Let ∫_-2^2(| sin x|+[x sin x]) d x=2(3- cos 2)+β, where [·] is the greatest integer function. Then β sin…2026
- Let (2^1-a+2^1+a), f(a),(3^a+3^-a) be in A.P. and α be the minimum value of f(a). Then the value of the…2026
- Let f(x)= {1/3, x ≤ π / 2; (b(1- sin x))/((π-2 x)^2), x>π / 2}. If f is continuous at x=π / 2, then the value…2026
- The value of the integral ∫_0^∞ (log_e(x))/(x^2+4) d x is:2026
- Let A= [1, 3, -1; 2, 1, α; 0, 1, -1] be a singular matrix. Let f(x)=∫_0^x(t^2+2 t+3) dt, x ∈[1, α]. If M and…2026
- The integral ∫_0^1 cot^-1(1+x+x^2) d x is equal to:2026
JEE Main 2026 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.