Question

What is wrong with the equation?

\(\int\limits_0^\pi {{{\sec }^2}xdx = \left( {\tan x} \right)} _0^\pi = 0\)

Short answer

Evaluation theorem cannot be applied.

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 \({\rm{\theta = \pi }}\)

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.