int_{0}^{frac{pi}{2}} frac{sin x cos x}{1+sin | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) $I = \int_{0}^{\frac{\pi}{2}} \frac{\sin x \cos x}{1+\sin ^{4} x} d x$ $I = \frac{1}{2} \int_{0}^{\frac{\pi}{2}} \frac{2 \sin x \cos x}{1+(\sin ^{

Vedclass · Accepted Answer

$\frac{\pi}{8}$

Vedclass · Answer

(B) $I = \int_{0}^{\frac{\pi}{2}} \frac{\sin x \cos x}{1+\sin ^{4} x} d x$ $I = \frac{1}{2} \int_{0}^{\frac{\pi}{2}} \frac{2 \sin x \cos x}{1+(\sin ^{2} x)^{2}} d x$ Let $\sin ^{2} x = t$,then $2 \sin x \cos x d x = dt$. When $x = 0$,$t = 0$ and when $x = \frac{\pi}{2}$,$t = 1$. $I = \frac{1}{2} \int_{0}^{1} \frac{dt}{1+t^{2}} = \frac{1}{2} [	an ^{-1} t]_{0}^{1}$ $I = \frac{1}{2} (	an ^{-1} 1 - 	an ^{-1} 0) = \frac{1}{2} (\frac{\pi}{4} - 0) = \frac{\pi}{8}$

$\int_{0}^{\frac{\pi}{2}} \frac{\sin x \cos x}{1+\sin ^{4} x} d x=$

Similar Questions

Considering four sub-intervals,the value of $\int_{0}^{1} \frac{1}{1+x} d x$ by Trapezoidal rule,is

Let $P(x) = x^2 + bx + c$ be a quadratic polynomial with real coefficients such that $\int_{0}^{1} P(x) dx = 1$ and $P(x)$ leaves a remainder of $5$ when divided by $(x-2)$. Then the value of $9(b+c)$ is equal to:

If $f(x) = \begin{cases} 4x + 3, & 1 \le x \le 2 \\ 3x + 5, & 2 < x \le 4 \end{cases}$,then $\int_1^4 f(x) \, dx = $

Let $[.]$ denote the greatest integer function. If $\int_0^{e^3}\left[\frac{1}{e^{x-1}}\right] d x=\alpha-\log _e 2$,then $\alpha^3$ is equal to . . . . . . .

The value of $\int_0^{\frac{\pi}{2}}|\sin x-\cos x| d x$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module