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