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How do you integrate #int (sec^2theta-sintheta)d theta#?

Answer 1

Aurora Alvarado

It is recommended that you know the following table of trig integrals by heart.

Separating the integrals:

#=int(sec^2theta)d theta - int(sin theta) d theta#

#= tan theta - (-costheta) d#

#= tan theta + costheta + C#

Hopefully this helps!

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Answer 2

Christopher Allers

To integrate ( \int (\sec^2(\theta) - \sin(\theta)) , d\theta ), you can use the following steps:

Recognize that ( \int \sec^2(\theta) , d\theta ) integrates to ( \tan(\theta) + C ), where ( C ) is the constant of integration.
For ( \int \sin(\theta) , d\theta ), integrate using the known result ( -\cos(\theta) + C ).
Combine the results from steps 1 and 2.

Therefore, the integral of ( \int (\sec^2(\theta) - \sin(\theta)) , d\theta ) is ( \tan(\theta) + \cos(\theta) + C ), where ( C ) is the constant of integration.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.