Use definite integrals and Fundamental Theorem of Calculus to find the exact area of the region between the graphs of $f ( x ) = \sin x$ and $g ( x ) = \cos x$ from x = 0 to x = $\pi$ /2.
A) $\sqrt { 2 } - 2$
B) $2 \sqrt { 2 } - 2$
C) $\sqrt { 2 } + 2$
D) $2 \sqrt { 2 } + 2$

Question

Quizplus · Accepted Answer

The area between the two curves from $x = 0$ to $x = \frac{\pi}{2}$ is found by integrating the difference between the functions over the given interval. Since $\cos(x) \geq \sin(x)$ in this interval, the area is given by $\int_{0}^{\frac{\pi}{2}} (\cos(x) - \sin(x)) dx$. Evaluating this integral gives $2\sqrt{2} - 2$.

Use Definite Integrals and Fundamental Theorem of Calculus to Find f(x)=sin⁡xf ( x ) = \sin xf(x)=sinx

Use Definite Integrals and Fundamental Theorem of Calculus to Find $f ( x ) = \sin x$