Question

Area between the curve $y = \cos x$ and $x -$axis when $0 \leq x$ is

• A. 2
• B. 4
• C. 0
• D. 3

Answer 1

Answer: (B)

4

Answer 2

$y = \cos x$, When $x \in \left[ 0 , \frac { \pi } { 2 } \right] , \cos x \geq 0$

When $x \in \left[ \frac { \pi } { 2 } , \frac { 3 \pi } { 2 } \right] , \cos x \leq 0$

When $x \in \left[ \frac { 3 \pi } { 2 } , 2 \pi \right] , \cos x \geq 0$

Thus required area is given by,

$\int _ { 0 } ^ { \pi / 2 } y d x = \int _ { 0 } ^ { \pi / 2 } \cos x d x + \int _ { \pi / 2 } ^ { 3 \pi / 2 } ( - \cos x ) d x + \int _ { 3 \pi / 2 } ^ { 2 \pi } \cos x d x$

unit