The area of the region bounded by the curve y | vedclass

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

Question

(C) The area $A$ of the region bounded by the curve $y = f(x)$,the $X$-axis,and the lines $x = a$ and $x = b$ is given by the integral: $A = \int_{a}^

Vedclass · Accepted Answer

$\frac{1}{2} \log 2$

Vedclass · Answer

(C) The area $A$ of the region bounded by the curve $y = f(x)$,the $X$-axis,and the lines $x = a$ and $x = b$ is given by the integral: $A = \int_{a}^{b} |y| \, dx$ Here,$y = 	an x$,$a = 0$,and $b = \frac{\pi}{4}$. Since $	an x \geq 0$ in the interval $[0, \frac{\pi}{4}]$,we have: $A = \int_{0}^{\frac{\pi}{4}} 	an x \, dx$ The integral of $	an x$ is $\ln|\sec x|$: $A = [\ln|\sec x|]_{0}^{\frac{\pi}{4}}$ $A = \ln|\sec(\frac{\pi}{4})| - \ln|\sec(0)|$ $A = \ln(\sqrt{2}) - \ln(1)$ $A = \ln(2^{1/2}) - 0$ $A = \frac{1}{2} \ln 2$ Thus,the correct option is $C$.

The area of the region bounded by the curve $y = \tan x$,$x = 0$,$x = \frac{\pi}{4}$,and the $X$-axis is . . . . . . sq. units.

Similar Questions

The area enclosed by the curve $y^2 + x^4 = x^2$ is :

The area (in square units) of the region bounded by the curve $y = |\sin 2x|$ and the $X$-axis in the interval $[0, 2\pi]$ is:

The area bounded by the curve $|y| + \frac{1}{2} = e^{-|x|}$ is

The area (in sq units) enclosed by the loop of the curve $ay^2 = x^2(a - x), (a > 0)$ is

If the area bounded by the curve $y = x^3 + ax$ (where $a > 0$), the $x$-axis, and the lines $x = -2$ and $x = 1$ is $\frac{37}{4}$ square units, find the value of $a$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module