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 bounded by the parabola $y^2 = 4ax$,its axis and two ordinates $x = 4$ and $x = 9$ is

If the area above the $x$-axis,bounded by the curves $y = 2^{kx}$,$x = 0$,and $x = 2$ is $\frac{3}{\ln 2}$,then the value of $k$ is

The area bounded by the curve $y=x^{3}$,the $X$-axis and the lines $x=1$ and $x=4$ is

The area bounded by the lines $y = x$,$x = -1$,$x = 2$ and the $x$-axis is

The area bounded by the curve $y = 4x - x^2$ and the $x$-axis is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module