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Numerade Educator

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Problem 65 Hard Difficulty

Evaluate the definite integral.

$ \displaystyle \int^a_0 x\sqrt{x^2 + a^2} \, dx $ $ (a > 0) $

Answer

$\frac{a^{3}(2 \sqrt{2}-1)}{3}$

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Video Transcript

okay, We know it could consider Are you to be what's under the square root, which is X squared plus a square, which means our d'you is to axe d x, which means x d x is 1/2. Do you only transfer the two over to the other side? Which means we can now pull out the constant of 1/2 and then we have are lower bound is zero squared plus a scored, which is a scored in the upper ground is a squared plus base chord which is two squared and we have the squirt of you. Do you? Okay? Take the powerful. Which means increase the exponents by one and divide by the new exponents. Now, using the fundamental damn of calculus, we know we can plug in.