If the value of the integral int -1 1 frac cos α x 1+3 x d x is 2/π . Then, a value of α is

Mathematics · Definite Integration

JEE Main 2024 — 4 April, Shift 2 — Question 11

If the value of the integral $\int_{-1}^{1} \frac{\cos \alpha x}{1+3^{x}} d x$ is $\frac{2}{\pi}$ . Then, a value of $\alpha$ is

Let $\mathrm{I}=\int_{-1}^{+1} \frac{\cos \alpha \mathrm{x}}{1+3^{\mathrm{x}}} \mathrm{dx}$

$I=\int_{-1}^{+1} \frac{\cos \alpha x}{1+3^{-x}} d x$

$\left(\operatorname{using} \int_{a}^{b} f(x) d x=\int_{a}^{b} f(a+b-x) d x\right)$

Add (1) and (II)

$2 I=\int_{-1}^{+1} \cos (\alpha x) d x=2 \int_{0}^{1} \cos (\alpha x) d x$

$I=\frac{\sin \alpha}{\alpha}=\frac{2}{\pi}($ given $)$

$\therefore \alpha=\frac{\pi}{2}$

Answer key and solution verified before publishing.

Start with this question, then two more from the same chapter — with a tutor that explains every step. Free.