What does it mean if you get 0 for improper

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SUMMARY

The integral of secant squared, ∫ secx² dx from 0 to π, results in tan(x) evaluated at the limits, yielding 0 for both tan(0) and tan(π). This indicates that the integral is improper due to the discontinuity at x = π/2, where the integrand is undefined. The conclusion is that the integral does not converge, and one must account for discontinuities by graphing the function before integration.

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Homework Statement



Question ∫ secx^2 dx from 0 to ∏ I get tanx and evaluate it using limits
lim tan(pi) - lim(tan(0)) I get 0 for both. What does it mean.

Homework Equations





The Attempt at a Solution




The integral doesn't converge? I know it doesn't but what does 0 mean. Maybe I did something wrong.
 
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Jbreezy said:

Homework Statement



Question ∫ secx^2 dx from 0 to ∏ I get tanx and evaluate it using limits
lim tan(pi) - lim(tan(0)) I get 0 for both. What does it mean.

Homework Equations





The Attempt at a Solution




The integral doesn't converge? I know it doesn't but what does 0 mean. Maybe I did something wrong.

The integrand is undefined at x = ##\pi/2##, which makes the integral an improper one. You can't just blithely integrate across a discontinuity.
 
Man! OK I know how to fix it I should graph first always with these.
 

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