The discussion revolves around the integral ∫(sec^2 x tanx) dx, specifically evaluated from 0 to ∏/3. Participants explore methods of integration, particularly focusing on integration by parts and potential substitutions.
The discussion is ongoing, with participants sharing insights about the integration process and the implications of their approaches. Some guidance has been offered regarding the oscillatory nature of the integral and the importance of recognizing this behavior in similar problems.
Participants note the relevance of understanding integration techniques and the potential for encountering similar questions in testing scenarios. There is an emphasis on the importance of recognizing patterns in integration results.
There is a direct u-sub to handle this integral, but the way you have done it does illustrate an important concept.LocalStudent said:When I did integration by parts I got to this:
tan^2 x - ∫(sec^2 x tanx) dx (integral also from 0 to ∏/3)
which take you back to the question I started with.
Jorriss said:Suppose, I = ∫Adx and you perform integration by parts and get I = B - ∫Adx. Well, that second integral is, as you noted, what you started with. Thus, I = B - I and so 2I = B and thus, I=B/2.
integrals.
Jorriss said:There is a direct u-sub to handle this integral, but the way you have done it does illustrate an important concept.
Suppose, I = ∫Adx and you perform integration by parts and get I = B - ∫Adx. Well, that second integral is, as you noted, what you started with. Thus, I = B - I and so 2I = B and thus, I=B/2.
That type of oscillatory behavior is very important for many trigonometric and exponential integrals.