Question

The area bounded by $y=\cos x,y=x+1$ and $y=0$ in the second quadrant is

• A. $\frac{3}{2}$ sq. units
• B. 2 sq. units
• C. 1 sq. unit
• D. $\frac{1}{2}$ sq,. units

Answer 1

The correct option is D $\frac{1}{2}$ sq,. units

$y=\cos x,y=x+1$ and $y=0$
Area of shaded region is required is (Area of curve OAB- area of ${△}^{le}$ OCB)
$\stackrel{0}{\underset{-\pi /2}{\int }}\cos xdx-\stackrel{0}{\underset{-1}{\int }}(x+1)dx$
$\sin x{|}_{-\pi /2}^0-(\frac{x^2}{2}+x){|}_{-1}^0$
$1-1/2=1/2squnits$