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 bounded by the curve $y = \cos x$ from $x = 0$ to $x = \pi$ is given by the integral of the absolute value of the function: $	ext{Area}

Vedclass · Accepted Answer

$2$ sq. unit

Vedclass · Answer

(C) The area bounded by the curve $y = \cos x$ from $x = 0$ to $x = \pi$ is given by the integral of the absolute value of the function: $	ext{Area} = \int_{0}^{\pi} |\cos x| \, dx$ Since $\cos x \ge 0$ for $x \in [0, \pi/2]$ and $\cos x \le 0$ for $x \in [\pi/2, \pi]$,we split the integral: $	ext{Area} = \int_{0}^{\pi/2} \cos x \, dx + \int_{\pi/2}^{\pi} (-\cos x) \, dx$ Evaluating the integrals: $= [\sin x]_{0}^{\pi/2} + [-\sin x]_{\pi/2}^{\pi}$ $= (\sin(\pi/2) - \sin(0)) + (-(\sin(\pi) - \sin(\pi/2)))$ $= (1 - 0) + (-(0 - 1))$ $= 1 + 1 = 2 	ext{ sq. units.}$

The area of the region bounded by the curve $y = \cos x$ between $x = 0$ and $x = \pi$ is

Similar Questions

The area of the region bounded by the parabola $y=x^2$ and the line $y=4$ is . . . . . . sq. units.

The area bounded between the parabola $y^{2}=4x$ and the line $y=2x-4$ is equal to

Find the area bounded by the curves $(x-1)^{2}+y^{2}=1$ and $x^{2}+y^{2}=1$.

The area (in sq. units) of the region bounded by the curves $y = 2^x$ and $y = |x + 1|$ in the first quadrant is

The area bounded by the curve $x(x^2 + p) = y - 1$ and the line $y = 1$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module