Find the area between the curves x=-2, x=3, y=4x, y=x-5

Those are all lines ...

So the x interval is from - 2 to 3, because of x=-2 and x=3

The upper line is y (u) = 4x and the lower line is y (l) = x-5

So the area between the two lines is:

A=⌠y (u) - y (l) dx

A=⌠4x-x+5 dx

A=⌠3x+5 dx

A=[3x^2/2+5x]

A=[ (3x^2+10x) / 2], x=[-2,3]

A = (1/2) (27+30 - (12-20))

A = (1/2) (57+8)

A = (1/2) (65)

A=32.5 u^2