integrate the function xy-3x-2y-10 with limits 3 to 4

Question

it is definite integral simply integrate it and subtract lower limit from upper limit

Answer 1

Because there are two variables I assume this is a double integral with the same limits applied to x and y:

∫∫(xy-3x-2y-10)dxdy.

Treat y as constant and integrate wrt x: x²y/2-3x²/2-2xy-10x and apply the limits:

8y-24-8y-40-(9y/2-27/2-6y-30)=-41/2+3y/2.

Now integrate wrt y: -41y/2+3y²/4 and apply the limits:

-82+12-(-123/2+27/4)=-61/4.

So the double-integral evaluates to -61/4.