Show that
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Originally Posted by liyi Show that well, by symmetry, the area "under" the curve is the same as the area "under" the curve of between the limits and . thus,
Or we can say So (This last it's easy to prove with a simple substitution.) Finally
A more interesting problem is so actually find, .
Originally Posted by ThePerfectHacker . I agree. I like this integral Define Set Now adding this integrals, For the last integral, make a substitution according to Since let's make a final substitution defined by for the second integral, so Therefore
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