Math-2414: Calculus II Practice on Section 8.6: Numerical Integration 1) Exploration. You are going to estimate the area A under the parabola on the interval [2, 3] by dividing the interval into 4 equal subintervals, building rectangles on those subintervals with height equal to the height of the function somewhere in the subinterval, and summing the area of the rectangles. a) First estimate A by using approximating rectangles with heights taken at the left endpoints. Will this be an underestimate or an overestimate? b) Now estimate A by using approximating rectangles with heights taken at the right endpoints. Will this be an underestimate or an overestimate? c) Now estimate A by using approximating rectangles with heights taken at the midpoints of the subintervals. Will this be an underestimate or an overestimate? d) Now estimate A by using the Trapezoidal Rule. Will this be an underestimate or an overestimate? e) Now estimate A by using the Simpson's Rule. Will this be an underestimate or an overestimate? Compare and contrast the estimation methods used. Which one appeared to be the most accurate? Reflect on your experiences.