The larger of the area bounded by y = cosx, y = x + 1 and y = 0 is

Options

A. `(1)/(2)` sq unit
B. `(3)/(2)` sq units
C. 1 sq unit
D. 2 sq units

Answer

B

Explanation

y = cos x and y = x + 1 meet at the point
(0,1), y = x + 1 passes through the points (-1,0) and [0,1], y=cosx meets X-axis at `((-pi)/(2),0)and((pi)/(2),0)`.

`therefore` Required area `=int_(-1)^(0)(x+1)dx+int_(0)^(pi//2)cosxdx`
`=[(x^(2))/(2)+x]_(-1)^(0)+[sinx]_(0)^(pi//2)`
`=0-((1)/(2)-1)+1=(3)/(2)` sq units.