While investigating ways to approximate definite integrals, it is
insightful to compare results to integrals whose exact values we know. To that end,
the following sequence of questions centers on

(a) Use the above applet to compute

(b) Likewise, use the applet to compute

(c) Use the Fundamental Theorem of Calculus to compute the exact value of

(d) We define the error in an approximation of a definite integral to be the difference
between the integral's exact value and the approximation's value. What is the error
that results from using

(e) Let us develop a new approach to estimating the
value of a definite integral known as the Trapezoid Rule. The basic idea is to use
trapezoids, rather than rectangles, to estimate the area under a curve. What is the formula for the area of a trapezoid with bases of length

Area of Trapizod

(f) Working by hand, estimate the area under

What is the error in this approximation?

How does it compare to the errors you calculated in (d)?

You can earn partial credit on this problem.