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(a) Graph the functions $ f(x) = \frac{1}{x^{1.1}} $ and $ g(x) = \frac{1}{x^{0.9}} $ in the viewing rectangles $ [0, 10] $ by $ [0, 1] $ and $ [0, 100] $ by $ [0, 1] $.

(b) Find the areas under the graphs of $ f $ and $ g $ from $ x = 1 $ to $ x = t $ and evaluate for $ t = 10, 100, 10^4 , 10^6 , 10^{10} $, and $ 10^{20} $.

(c) Find the total area under each curve for $ x \ge 1 $, if it exists.

a.

b. 990

c. $g(x)=\frac{1}{x^{0.9}}$ for $x \geq 1$ does not exist.

Integration Techniques

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Harvey Mudd College

University of Michigan - Ann Arbor

Idaho State University

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