Mathematics · 2024
JEE Main · 27 January 2024, Shift 2 · Q12
For 0< a <1, the value of the integral ∫_0^π (d x)/(1-2 a cos x+ a^2) is:
For $\displaystyle 0<\mathrm{a}<1$, the value of the integral $\displaystyle \int_0^\pi \frac{\mathrm{d} x}{1-2 \mathrm{a} \cos x+\mathrm{a}^2}$ is :
Official answer
From NTA’s final answer key for this paper.
(3)
$\displaystyle \frac{\pi}{1-a^2}$
More from Definite Integration
- ∫_0^π / 4 (cos^2 x sin^2 x)/(( cos^3 x+ sin^3 x)^2) d x is equal to2024
- 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
- If the value of the integral ∫_-1^1 (cos α x)/(1+3^x) d x is 2/(π). Then, a value of α is2024
- If (a, b) be the orthocentre of the triangle whose vertices are (1,2),(2,3) and (3,1), and I_1=∫_a^b x sin (4 x-x^2) d x, I_2=∫_a^b sin (4 x-x^2) d…2024
- 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
JEE Main 2024 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.