If the area of the region bounded by the para | vedclass

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

Question

(B) The area $A$ bounded by the parabola $y^2 = 4kx$ and the line $x = k$ is given by $A = 2 \int_{0}^{k} \sqrt{4kx} \, dx$.$A = 2 \cdot 2\sqrt{k} \in

Vedclass · Accepted Answer

$\frac{\pi}{6}$

Vedclass · Answer

(B) The area $A$ bounded by the parabola $y^2 = 4kx$ and the line $x = k$ is given by $A = 2 \int_{0}^{k} \sqrt{4kx} \, dx$.$A = 2 \cdot 2\sqrt{k} \int_{0}^{k} x^{1/2} \, dx = 4\sqrt{k} \left[ \frac{x^{3/2}}{3/2} \right]_{0}^{k}$.$A = 4\sqrt{k} \cdot \frac{2}{3} k^{3/2} = \frac{8}{3} k^2$.Given $A = \frac{128}{3}$, so $\frac{8}{3} k^2 = \frac{128}{3}$.$8k^2 = 128 \implies k^2 = 16 \implies k = 4$ (since $k > 0$).We need to find $\sin^{-1}(\frac{2}{k}) = \sin^{-1}(\frac{2}{4}) = \sin^{-1}(\frac{1}{2})$.$\sin^{-1}(\frac{1}{2}) = \frac{\pi}{6}$.

If the area of the region bounded by the parabola $y^2 = 4kx$ and the line $x = k$ (where $k > 0$) is $\frac{128}{3} \text{ sq. units}$, then the value of $\sin^{-1}(\frac{2}{k})$ is equal to...

Similar Questions

The principal value of $\cot^{-1}\left(\frac{-1}{\sqrt{3}}\right)$ is equal to . . . . . . .

If $\frac{\pi}{2} \le x \le \frac{3\pi}{2},$ then $\sin^{-1}(\sin x)$ is equal to

$\tan ^{-1}\left(\tan \frac{31 \pi}{6}\right)=$ . . . . . . .

If $y = \cos^{-1}(\sin x)$, where $\frac{\pi}{2} < x < \pi$, then $\frac{dy}{dx} = \dots$

$\sec \left(\tan ^{-1} \frac{y}{2}\right) = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module