A curve C is mapped by the equation ( 1+x)(4-x). The curve intersects the x-axis at x = –1 and x = 4. A region R is bounded by C and the x-axis. Use calculus to find the exact area of R.
First draw the curve. Figure out and write the integration problem. Integral4-1 (1+x)(4-x) dx.Expand integral4-1 4 + 3x - x2 dx.= 4-1[4x + 3x2/2) -x2] = 16 + 30 - 64/3 - (-4 + 3/2 + 1/3)= 125/6
