The integral of u√(1+u²) du can be solved using the method of substitution. The correct answer is (1/3)(1 + u²)^(3/2). To derive this, one should let v = 1 + u², which leads to dv = 2u du, allowing for a straightforward substitution. This method emphasizes the importance of recognizing when to apply substitution multiple times for complex integrals.
PREREQUISITESStudents studying calculus, particularly those focusing on integration techniques, as well as educators looking for examples of substitution in integrals.
What's the derivative of 1+u2 ?Rosebud said:
The derivative of 1+u^2 with respect to u is 2u du.SammyS said:
Do you know the method of substitution ?Rosebud said:
No.SammyS said:
That should have been a BIG hint.Rosebud said:
Thanks for the tip. I did that but I still fail to see the connection. Can you, or someone else, give me the next step?SammyS said:
Numerator? There is no fraction here unless you you consider 1 as the denominator.DeldotB said:
ahh, thought I saw a / in front of the root.Rosebud said:
That helped immensely. Thank you so much. I forgot that I could use substitution more than once.Rosebud said:
SammyS said:
So, you do know substitution.Rosebud said:
Rosebud said:
Yes, I know substitution. You asked me if I knew the method of substitution, which I understood as, you asking if I knew which method of substitution that I should use.SammyS said: