Question

Will give many points if you can help me

Answer 1

38

Explanation:

You're simply subtracting areas.

`\int \limits_4^(12)x dy`

represent the blue area in the edited photo. Which you can get from an area of the rectangle with opposite corners in the origin and in Q(6;12) (with red sides, which has area 6x12=72) minus the area of the green rectangle of opposite corners origin and P(1;4) (of area 1x4=4), minus the area limited by y=0, y=f(x), x=1 and x=6, which is, as you know, the integral you've been given at the start, 30.

Area is thus 72 - 4 - 30 = 38

(yes, I did it with paint, the image should be understandable hopefully)