## calc integration

question and work is here

I got the answer down to letter A and D. Now I feel like it's letter A but not sure...

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 Youre asking if $$\frac{sin^2(x)}{2} = \frac{-cos(2x)}{4}$$ Try x = 0 Or notice that f(x) = sin(x)cos(x) = sin(2x)/2, then the integral is real easy.
 Blog Entries: 9 Recognitions: Homework Help Science Advisor The easiest method is to differentiate each of the 3 results... "D" is the correct answer. Daniel.

## calc integration

Take the derivative of each of the choices.

*Haha, too late

 Quote by whozum Youre asking if $$\frac{\sin^2{x}}{2}=\frac{-\cos 2x}{4}$$
Not at all. If F(x) is an antiderivative of f(x) then so is F(x)+C for any C. Here,

$$\frac{\sin^2 x}{2} = \left(-\frac{\cos 2x}{4}\right) + \frac{1}{4}$$

 Quote by dextercioby The easiest method is to differentiate each of the 3 results... "D" is the correct answer. Daniel.
how did you get III to be true?

 look at my last post.
 Convert f(x) to what I recommended and the integral evaluates to D directly.

 Quote by Data Not at all. If F(x) is an antiderivative of f(x) then so is F(x)+C for any C. Here, $$\frac{\sin^2 x}{2} = \left(-\frac{\cos 2x}{4}\right) + \frac{1}{4}$$
Good call, I didnt see that.