Question

given
integral 18x sqrt(x^2 +1) dx from 0 to 1 =12 sqrt(2) -6

evaluate
integral 18u sqrt(u^2 +1) du from 0 to 1

This is all the question had on it and I am not sure what it is asking. Any help is greatly appreciated thanks!

Answer 1

Im guessing that what it means is when you would solve the first integral, you would normally say u = x^2+1, du = 2xdx, etc. So Im guessing they want you to use that same ufor the second integral. Integrate like normal, let v = u^2 + 1, dv = 2udv and then at the very end, recognize that u = x^2 + 1because that would have been the u-substitution initially.

Answer 2

thanks this helped!