Answer A or D for Calc Integration Question

[UrbanXrisis]

question and work is http://home.earthlink.net/~urban-xrisis/clip_image002.jpg

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

 

[whozum]

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.

 

[dextercioby]

The easiest method is to differentiate each of the 3 results...

"D" is the correct answer.

Daniel.

 

[Knavish]

Take the derivative of each of the choices.

*Haha, too late

 

[Data]

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,

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

 

[UrbanXrisis]

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?

 

[Data]

look at my last post.

 

[whozum]

Convert f(x) to what I recommended and the integral evaluates to D directly.

 

[whozum]

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.