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Expert-verified Found in: Page 289 ### Essential Calculus: Early Transcendentals

Book edition 2nd
Author(s) James Stewart
Pages 830 pages
ISBN 9781133112280 # What is wrong with the equation?$$\int\limits_0^\pi {{{\sec }^2}xdx = \left( {\tan x} \right)} _0^\pi = 0$$

Evaluation theorem cannot be applied.

See the step by step solution

## Step 1:What’s given.

Given Function is $${\rm{f(x) = se}}{{\rm{c}}^{\rm{2}}}{\rm{xdx}}$$from $${\rm{(\pi ,0)}}$$

Here $$\int\limits_{\rm{0}}^{\rm{\pi }} {} {\rm{se}}{{\rm{c}}^{\rm{2}}}{\rm{xdx}}$$does not exist because the function $${\rm{f(\theta ) = se}}{{\rm{c}}^{\rm{2}}}{\rm{\theta }}$$has an infinite discontinuity at $${\rm{\theta = 0}}$$ and $${\rm{\theta = \pi }}$$

## Step 2: Checking for Discontinuity.

That is, $${\rm{f}}$$is discontinuous on the interval $${\rm{(\pi ,0)}}$$

Since $${\rm{f}}$$ is discontinuous, evaluation theorem cannot be applied. ### Want to see more solutions like these? 