Let A denote the area enclosed by the graph $f ( x ) = \cos x,$ the x-axis, and the lines $x = 0$ and $x = \frac { \pi } { 2 }$ . By part 2 of the Fundamental Theorem of Calculus, A is

A) $\frac { 1 } { 2 }$
B)1
C) $\frac { 3 } { 2 }$
D) $\frac { \pi } { 2 }$
E) $\pi$

Question

Let A denote the area enclosed by the graph $f ( x ) = \cos x,$ the x-axis, and the lines $x = 0$ and $x = \frac { \pi } { 2 }$ . By part 2 of the Fundamental Theorem of Calculus, A is

A) $\frac { 1 } { 2 }$
B)1
C) $\frac { 3 } { 2 }$
D) $\frac { \pi } { 2 }$
E) $\pi$

Quizplus · Accepted Answer

The area A can be found by integrating $f(x) = \cos x$ from $x = 0$ to $x = \frac{\pi}{2}$. The integral of $\cos x$ is $\sin x$, so evaluating this from 0 to $\frac{\pi}{2}$ gives $\sin(\frac{\pi}{2}) - \sin(0) = 1 - 0 = 1$.

Let a Denote the Area Enclosed by the Graph f(x)=cos⁡x,f ( x ) = \cos x,f(x)=cosx,

Let a Denote the Area Enclosed by the Graph $f ( x ) = \cos x,$