Mathematics · 2025
JEE Main · 2 April 2025, Shift 2 · Q19
Let ( a, b ) be the point of intersection of the curve x^2=2 y and the straight line y-2 x-6=0 in the second quadrant. Then the integral I =∫_a^b (9…
Let $\displaystyle (\mathrm{a}, \mathrm{b})$ be the point of intersection of the curve $\displaystyle x^2=2 y$ and the straight line $\displaystyle y-2 x-6=0$ in the second quadrant. Then the integral $\displaystyle \mathrm{I}=\int_{\mathrm{a}}^{\mathrm{b}} \frac{9 x^2}{1+5^x} \mathrm{~d} x$ is equal to :
Official answer
From NTA’s final answer key for this paper.
(3)
$\displaystyle 24$
More from Definite Integration
- If ∫_0^1 4 cot^-1(1-2 x+4 x^2) d x=a tan^-1(2)-b log_e(5), where a, b ∈ N, then (2 a+b) is equal to ____.2026
- Let for f(x)=7 tan^8 x+7 tan^6 x-3 tan^4 x-3 tan^2 x, I_1=∫_0^π / 4 f(x) d x and I_2=∫_0^π / 4 x f(x) d x. Then 7 I_1+12 I_2 is equal to:2025
- The integral 80 ∫_0^((π)/4)((sin θ+ cos θ)/(9+16 sin 2 θ)) d θ is equal to:2025
- The value of ∫_-π / 6^π / 6((π+4 x^11)/(1- sin (|x|+π / 6))) d x is equal to:2026
- Let [·] denote the greatest integer function and f(x)= lim_n → ∞ 1/(n^3) Σ_k=1^n[(k^2)/3^x]. Then 12 Σ_j=1^∞ f(j) is equal to ____.2026
- If f(x) satisfies the relation f(x)=e^x+∫_0^1(y+x e^x) f(y) d y, then e+f(0) is equal to ____.2026
- Let f: R → R be a twice differentiable function such that f(2)=1. If F(x)=x f(x) for all x ∈ R, ∫_0^2 x F^′(x) d x=6 and ∫_0^2 x^2 F^′ ′(x) d x=40,…2025
- The value of ∫_-1^1 ((1+√(|x|-x)) e^x+(√(|x|-x)) e^-x)/(e^x+e^-x) d x is equal to2025
JEE Main 2025 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.