Question

Find area under the curve? Pl refer to the question in the img attached

Answer 1

`A=49`

Explanation:

.

This is a piece-wise function. We have to find the area under each piece separately and add them up.

`y=-1`

The area under this piece from `-2` to `0` is:

`A_1=int_-2^0 -dx=-x=-(0)-(-(-2))=0-2=-2`

`y=(x+2)^2`

The area under this piece from `0` to `3` is:

`A_2=int_0^3(x+2)^2dx`

Let `u=x+2`, then `du=dx`

`A_2=intu^2du=1/3u^3=1/3(x+2)^3=1/3(3+2)^3-1/3(0+2)^3`

`A_2=125/3-8/3=117/3=39`

`y=x`

The area under the curve for this piece from `3` to `5` is:

`A_3=int_3^5xdx=1/2x^2=1/2(5)^2-1/2(3)^2=25/2-9/2=16/2=8`

Area under the piece-wise function is:

`A=A_1+A_2+A_3=2+39+8=49`