Mathematics · 2023
JEE Main · 15 April 2023, Shift 1 · Q10
If ∫_0^1 1/((5+2 x-2 x^2)(1+e^(2-4 x))) d x=1/(α) log_e((α+1)/(β)), α, β>0, then α^4-β^4 is equal to
If $\displaystyle \int_0^1 \frac{1}{\left(5+2 x-2 x^2\right)\left(1+e^{(2-4 x)}\right)} d x=\frac{1}{\alpha} \log _e\left(\frac{\alpha+1}{\beta}\right), \alpha, \beta>0$, then $\displaystyle \alpha^4-\beta^4$ is equal to
Official answer
From NTA’s final answer key for this paper.
(4)
$\displaystyle 21$
More from Definite Integration
- Let the function f:[0,2] → R be defined as f(x)= {e^min {x^2, x-[x]}, x ∈[0,1); e^[x- log_e x], x ∈[1,2]} where [t] denotes the greatest integer less…2023
- The value of k ∈ N for which the integral I_n=∫_0^1(1-x^k)^n d x, n ∈ N, satisfies 147 I_20=148 I_21 is2024
- ∫_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 f(x) be a function satisfying f(x)+f(π-x)=π^2, ∀ x ∈ R. Then ∫_0^π f(x) sin x d x is equal to2023
- 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
- lim_n → ∞[1/(1+n)+1/(2+n)+1/(3+n)+…+1/(2 n)] is equal to2023
JEE Main 2023 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.