Find the area of the region bounded by the given curves. $y=\cos x, y=\sin 3 x, x=0, x=\frac{\pi}{2}$
A) $\frac{1}{4}$
B) $\frac{1}{2}$
C) 4
D) 2
E) $\frac{1}{3}$

Question

Quizplus · Accepted Answer

To find the area between the curves $y = \cos x$ and $y = \sin 3x$ from $x = 0$ to $x = \frac{\pi}{2}$, we calculate the integral of the absolute difference of the functions over the interval. The area is given by $\int_0^{\frac{\pi}{2}} |\cos x - \sin 3x| \, dx$. Evaluating this integral yields $\frac{1}{2}$.

Find the Area of the Region Bounded by the Given y=cos⁡x,y=sin⁡3x,x=0,x=π2y=\cos x, y=\sin 3 x, x=0, x=\frac{\pi}{2}y=cosx,y=sin3x,x=0,x=2π​

Find the Area of the Region Bounded by the Given $y=\cos x, y=\sin 3 x, x=0, x=\frac{\pi}{2}$