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exploration4

exploration4 - Exploration 4 Definite Integrals by...

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Exploration 4 Definite Integrals by Trapezoidal Rule Rocket Problem: Ella Vader (Darth’s daughter) is driving in her rocket ship. At time t = 0 minutes she fires her rocket engine. The ship speeds up for a while, then slows down as Alderaan’s gravity takes its effect. The graph of her velocity, v(t) miles per minute, is shown below. 1. What mathematical concept would be used to estimate the distance Ella goes between t = 0 and t = 8? 2. Estimate the distance in Problem 1 geometrically. 3. Ella figures that her velocity is given by v(t) = t 3 - 21t 2 + 100t + 110 Plot this graph on your calculator. Does the graph confirm or refute what Ella figures? Tell how you arrive at your conclusion. 4. Divide the region under the graph from t = 0 to t = 8, which represents the distance, into four vertical strips of equal width. Draw four trapezoids whose areas approximate the areas of these strips, and whose parallel sides extend from the x-axis to the graph. By finding the areas of these trapezoids, estimate the distance Ella goes.

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