Improper Integrals: Example 6: sec(x)

In this video I go over another example on improper integrals and this time solve the integral of the function sec(x) from x = 0 to x = π/2. This function has a vertical asymptote at x = π/2 because sec(x) approaches infinite as x approaches π/2, thus making it a Type 2 improper integral. Solving this by first writing it as a limit of a definite integral yields a divergent integral because the limit approaches infinite. In this particular integral, the divergent limit represents an infinite area under the curve.

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Related Videos:

Improper Integrals Example 5: 1/sqrt(x-2): https://youtu.be/C8X_TUdTo-A Improper Integrals: Type 2: Discontinuous Integrands: https://youtu.be/livlGUBuM54 Improper Integrals: Introduction: https://youtu.be/ud44W-0jC-c The Definite Integral - Brief Introduction: http://youtu.be/vhMP5SKbQjU Integrals and Areas Between Curves: http://youtu.be/2F03KMLIzbk Infinite Limits - Precise Definition: http://youtu.be/QyVTgSzn7dE Infinite Limits - Vertical Asymptotes: http://youtu.be/H-5Txa8SOwQ Trigonometric Identity: Integral of sec(x): http://youtu.be/s-AyOdd9kuc Trigonometry: Sine, Cosine and Tan Functions: http://youtu.be/WKTIlF2oWw8 .

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