How would I begin to solve this integrand ? by completing the square ?
I try completing the square when I factor out a - 4 outside the square root but it does not work out quite right.
This one is just a tad confusing to me when trying to complete the square, which I would assume would be the best way to do this.
I dont really know where fantastic is going with his tip but the problem looks like an arcsin/arccos to me,
the definition is:
derivative of arcsin(x) is:
derivative of arccos(x) is:
Make it look like 1 + something^2 in the square root and the solution should not be far away.
First, check that 5 - (2x - 3)^2 really equals what it must; second, in fantastic's post, just before he obtained this expression, he took out (1/4) from the parentheses but here he got;
[5/4 - (x - 3/2)^2] = [5/4 - ((2x - 3)/2)^2] = [5/4 - (1/4)(2x-3)^2] and now 1/4 goes out and etc.
If you follow what's been posted in this thread then it should be clear that you have a standard form. I had hoped the basic substitution u = 2x - 3 would have made that obvious. I suggest you go back and review this material.