a Find an approximation to the integral using a Riemann sum with right endpoints and n 8 Rg 1 5 b Draw a diagram to illustrate the approximation in part a y y 5r 3 2 1 2 0 31 4 3 2 1 3x dx 2 O 34 1 2 1 3 2 2 5 2 3 c Consider the following theorem 2 7 2 Use this to evaluate the integral 4 4 If fis integrable on a b then 4 2 9 5 5 5 4 3 2 4 3 2 2 0 3 f x dx f x dx lim x Ax where Ax n l 3 2 d Interpret the integral in part c as a difference of areas The integral represents the area below the x axis minus the area above the x axis O The Integral represents the area above the x axis minus the area below the x axis 4 9 9 5 x b a and x a AX n