Area between curves Let R be the region bounded by the graphs of y = x−p and y = x−qfor x≥ 1, where q > p > 1. Find the area of R.

Problem 56E

Area between curves Let R be the region bounded by the graphs of y = and y = for x ≥ 1, where q > p > 1. Find the area of R.

Answer;

Step-1;

Let R be the region bounded by the graph of y = and y =for x ≥ 1, where q > p > 1.

Now , we have to find out the area between the curves.

Given q > p > 1, in the interval [1, infinity), the graph of will always be above the graph of . So the setup of the area integral is ∫( − )dx from 1 to ∞. This can be rewritten as the difference of two integrals:

=

= -

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