you didn't do anything wrong.
graph and
... what do you see?
Hi,
When integrating 2sin(x)cos(x), I used a simple u sub and got sin^2(x), no big deal. However when I pop this into wolfram, it results in (-1/2)cos(2x). This is the link Wolfram Mathematica Online Integrator
I take the derivative of what wolfram gives me and it certainly is not 2sin(x)cos(x). Can someone tell me what I did wrong please?
Hello, pberardi!
This is a classic problem/puzzle . . .When integrating , I used a simple u sub and got
However when I pop this into wolfram, it results in: .
You had: .
. . You let:
. . Substitute: .
. . Back-substitute: .
We also have: .
. . Let:
. . Substitute: .
. . Back-substitute: .
We have the identity: .
So: .
And all three answers are correct!
Ok that all makes sense, so they are the same function. But why is it that when I plug in pi/4 in sin^2(x) I get 1/2 and when I plug in pi/4 into (-1/2)cos(2x), I get 0? Shouldn't they give me the same answer? I know this is silly and I am probably just making a stupid error somewhere but I dont know where.