Question

# If [ ] denotes the greatest integer function then the integral $$\displaystyle \int_{0}^{\pi}[cos x]dx$$ is equal to :

A
π2
B
0
C
1
D
π2

Solution

## The correct option is D $$-\dfrac {\pi}{2}$$We know that for $$\cos x\in [0,\dfrac {\pi}{2}]\Rightarrow 1\ge \cos x \ge 0$$ and $$\cos x\in [\dfrac {\pi}{2},\pi]\Rightarrow 0\ge \cos x \ge -1$$$$\displaystyle \int _{ 0 }^{ \pi }{ [\cos { x]dx= } } \displaystyle \int _{ 0 }^{ \tfrac { \pi }{ 2 } }{ 0dx\quad + } \displaystyle \int _{ \tfrac { \pi }{ 2 } }^{ \pi }{ -1dx}$$$$=-\dfrac { \pi }{ 2 }$$  Mathematics

Suggest Corrections

0

Similar questions
View More

People also searched for
View More