Question

The area (in sq. units) bounded by $y=\cos x,y=1+x$ and $x-$axis is

• A. $1$
• B. $\frac{1}{2}$
• C. $\frac{3}{2}$
• D. $2$

Answer 1

The correct option is C $\frac{3}{2}$


The required area$=\underset{-1}{\overset{0}{\int }}(1+x)dx+\underset{0}{\overset{\pi /2}{\int }}\cos xdx$

$={[x+\frac{x^2}{2}]}_{-1}^0+[\sin x{]}_0^{\pi /2}=-(-1+\frac{1}{2})+1=\frac{3}{2}\text{sq. units}$