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

X^2 - 4x +(4/2^2) + y^2 + 8y + (8/2^2) = -4 + (4/2^2) + (8/2^2)(x + 2)^2 + (y + 4)^2 = -4 + 4 + 16your center is (-2, -4) and the radius is the sqrt of -4 + 4 + 16 which is 4