If the area of the region `{(x , y):0lt=ylt=x^2+1,0lt=ylt=x+1,0lt=xlt=2}` is `A` , then the value of `3A-17` is____

Answer

6

Explanation

Draw the given region point of intersection of `y=x^(2)+1`
`y=x+1`
`x+1=x^(2)+1`
`x=0,1`

`"Required area "OABCDE=overset(1)underset(0)int(x^(2)+1)dx+overset(2)underset(1)int(x+1)dx`
`=((x^(3))/(3)+x)_(0)^(1)+((x^(2))/(2)+x)_(1)^(2)=(23)/(6)` sq. units