Trapezoidal Rule .. help help Calculus?

Question

http://www.jamesrahn.com/CalculusI/Activities/LABS/trapezoidal%20rule.pdf
can someone tell me how to answer example 1 plz ??

I have the same problem in my hw and I can't solve it .. plz help .. my teacher checks hw everyday!!

Answer 1

You're supposed to approximate the volume of the pond. Since we know only its average depth is 20 ft, we will assume that its depth everywhere is 20 ft. So the volume equals the depth times the surface area, and the surface area is what is to be approximated by trapezoidal rule. Specifically, each of the "strips" shown in the diagram is to be approximated by a trapezoid. The straight borders are the bases of the trapezoids, and the 200 ft spacing is the height of each trapezoid.

The area of a trapezoid is half the height times the sum of the bases. So, adding up the areas of all the trapezoids, the area of the pond is approximately

½(200)[(0+520) + (520+800) + (800+1000) + ... + (860+0)]

which can be written

½(200)[0 + 2*520 + 2*800 + 2*1000 + ... + 2*860 + 0]

I'll let you do the arithmetic. Then multiply the above result by the assumed depth of 20 ft to get the approximate volume of the pond.