Question
The value of $$\int_{ - 1}^1 {\max \left\{ {2 - x,\,2,\,1 + x} \right\}} $$ is :
A.
4
B.
$$\frac{9}{2}$$
C.
2
D.
none of these
Answer :
$$\frac{9}{2}$$
Solution :
$$\eqalign{
& I = \int_{ - 1}^0 {\max \left\{ {2 - x,\,2,\,1 + x} \right\}} dx + \int_0^1 {\max \left\{ {2 - x,\,2,\,1 + x} \right\}} dx \cr
& \,\,\,\,\, = \int_{ - 1}^0 {\left( {2 - x} \right)dx} + \int_0^1 {2\,dx} \cr
& \,\,\,\,\, = \left[ {2x - \frac{{{x^2}}}{2}} \right]_{ - 1}^0 + 2\left[ x \right]_0^1 \cr
& \,\,\,\,\, = - \left( { - 2 - \frac{1}{2}} \right) + 2 \cr
& \,\,\,\,\, = \frac{9}{2} \cr} $$