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Math Help - Integrating trig functions

  1. #1
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    Integrating trig functions

    This question is more about my understanding than solving. I've done the question asking me to show that the differential of cotx is -cosec^2x by putting it in the form cosx/sinx. Then the second part says "Hence find the exact value of the integral of cot^2x between pi/2 and pi/4". I don't really see how the first part helps with that.

    Many thanks in advance.
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  2. #2
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    Quote Originally Posted by JeWiSh View Post
    This question is more about my understanding than solving. I've done the question asking me to show that the differential of cotx is -cosec^2x by putting it in the form cosx/sinx. Then the second part says "Hence find the exact value of the integral of cot^2x between pi/2 and pi/4". I don't really see how the first part helps with that.

    Many thanks in advance.
    From the basic Pythagorean identity: \int_{\pi/4}^{\pi/2} \text{cot}^2 (x) \, dx = \int_{\pi/4}^{\pi/2} \text{cosec}^2 (x) - 1 \, dx.

    And from the previous answer you know what the integral of \text{cosec}^2 (x) is ....
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