Question

The area bounded by $y=x+1$ and $y=\cos x$ and the $x$-axis, is

• A. $1\text{sq. unit}$
• B. $\frac{3}{2}\text{sq. unit}$
• C. $\frac{1}{4}\text{sq. unit}$
• D. $\frac{1}{8}\text{sq. unit}$

Answer 1

The correct option is B $\frac{3}{2}\text{sq. unit}$

The graph of $y=\cos x$ and $y=x+1$ as shown below
We have to find the area of the shaded region:
$A=\frac{1}{2}\times 1\times 1+\underset{0}{\overset{\pi /2}{\int }}\cos xdx=\frac{1}{2}+1=\frac{3}{2}\text{sq. unit}$