int_0^{pi /6} frac{sin x}{cos^3 x} , dx = | vedclass

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

Question

(B) Let $I = \int_0^{\pi /6} \frac{\sin x}{\cos^3 x} \, dx = \int_0^{\pi /6} 	an x \sec^2 x \, dx$. Substitute $t = 	an x$. Then $dt = \sec^2 x \, d

Vedclass · Accepted Answer

$\frac{1}{6}$

Vedclass · Answer

(B) Let $I = \int_0^{\pi /6} \frac{\sin x}{\cos^3 x} \, dx = \int_0^{\pi /6} 	an x \sec^2 x \, dx$. Substitute $t = 	an x$. Then $dt = \sec^2 x \, dx$. When $x = 0$,$t = 	an(0) = 0$. When $x = \pi/6$,$t = 	an(\pi/6) = 1/\sqrt{3}$. Thus,$I = \int_0^{1/\sqrt{3}} t \, dt = \left[ \frac{t^2}{2} ight]_0^{1/\sqrt{3}} = \frac{1}{2} \left( \frac{1}{\sqrt{3}} ight)^2 - 0 = \frac{1}{2} 	imes \frac{1}{3} = \frac{1}{6}$.

$\int_0^{\pi /6} \frac{\sin x}{\cos^3 x} \, dx = $

Similar Questions

$\int_{1}^{e} \frac{dx}{x(1+\log x)^{2}} =$

The value of the integral $\int_{1/\pi }^{2/\pi } \frac{\sin(1/x)}{x^2} \,dx$ is:

If $k \int_{0}^{1} x \cdot f(3x) \, dx = \int_{0}^{3} t \cdot f(t) \, dt$,then the value of $k$ is

$\int_{\pi /4}^{\pi /2} \cos \theta \csc^2 \theta \, d\theta = $

Let $\frac{d}{dx}F(x) = \frac{e^{\sin x}}{x}$ for $x > 0$. If $\int_{1}^{4} \frac{3}{x} e^{\sin(x^3)} dx = F(k) - F(1)$,then one of the possible values of $k$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module