Integration of sin(x)cos(x)?

Question

Which of the followings are integrals of f(x) = sin(x)cos(x)?

I. F(x) = cos(2x)/4

2. F(x) = cos^2(x)/2

3. F(x) = sin^2(x)

Thank you for your help!

Answer 1

Let u = sin(x)

Then du = cos(x) dx

Integration of sin(x) cos(x) dx becomes

integration of u du which gives us u^2 / 2

which is sin^2 (x) / 2

Therefore none of the above are correct or your problem was written incorrectly.

Thanks

Answer 2

should be number "2", but my answer shows up as a negative...

answer my question plz.

http://answers.yahoo.com/question/index;...

Answer 3

Using u=sin(x)  for substitution, we get

du=cos(x)

so we integrate      u du        (after substituion from you original question)

integral of udu=1/2u^2+C

now we substitue u back to   u = sin(x)  and we get:

1/2sin^2(x)+C

then we can multiply the whole equation with "2"

and we'll get:

sin^2(x) + C1

and I would pick answer #3....  however, you are missing a constant so......

good luck

Answer 4

We have:

∫f(x)dx =

∫sin(x)cos(x)dx =

∫sin(x)d(sin(x)) =

sin²(x)/2 + C ;

hence,

none of the above.

Answer 5

None- they're close but missing negative signs.

ANSWER

Answer 6

u=sinx

du=cosx

int(udu=1/2u^2+C

1/2sin^2(x)+C

seeing as none of them have +C, its none of the above.

make it a good day