Question

Find intergral sin(x)cos(x)

Answer 1

write sin x cos x as sin 2x / 2
and integrate

Answer 2

First step is to take the constant out which is?

Answer 3

why sin2x /2? is that one of the trig identity

Answer 4

sin2x = 2 sin x cos x is a standard identity

Answer 5

Yes.

Answer 6

http://screencast.com/t/g6dNJGxjezEf

Answer 7

\[\sin (2x) = 2\sin x \cos x\]Divide both sides by 2.

Answer 8

but there is a 2..u can just divide it out..?

Answer 9

ohh..dont know i can do that.. ok thanks everyone

Answer 10

No, but you can take it outside.

Answer 11

sin(2x)/2 = 1/2 * sin(2x)
Since 1/2 is a constant, you can take it out of the integral.

Answer 12

oh ok thanks. i get it

Answer 13

Now, what's the integral of sin(2x)?

Answer 14

-cosx

Answer 15

-cos(2x)**

Answer 16

oh , 2x, then just 1/2

Answer 17

-cos(2x) + C**

Answer 18

or u can do what @baldymcgee6 has posted

Answer 19

\[\rm \left({1 \over 2} \times -\cos(2x) \right)+ C\]

Answer 20

@hartnn He hasn't done it. It's WolframAlpha.

Answer 21

It's a shame how people who use machines get medals.

Answer 22

but cos(2x) is different from cos^2 (X) right

Answer 23

Yes.

Answer 24

haha, u guys all deserve medals :D really helpful

but wolframalpha 's answer is in cos^2(x)
here is in 2x

Answer 25

Never mind wolframalpha.

Answer 26

And you're welcome. :)

Answer 27

<Vulcan greet>