Question

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

Answer 1

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