[jackie11]

Hi there

I have the question:



I know that sin x integrated is - cos x,

so is the answer to my question, before working out the exact values with the limits, this;



Many thanks

[gridlock]

The integral of sin(ax+b) is -(1/a)cos(ax+b).
That means in this situation a is 1/3.

[jackie11]

ok so in my case its -3 cos x ??

[gridlock]

The x value must remain the same as 'a' remains in front it.

[jackie11]

so its -3 cos 1/3x which is - cos x??

[gridlock]

Yes and no. Cos(ax) is one value and 'a' cannot be changed by the value cos is multiplied by. The answer is -3cos(x/3). There's also a '+ c' but you already knew that. :P

[jackie11]

ok thank you very much

[gridlock]

(Original post by jackie11)
ok thank you very much

No problem; thanks for the rep.

[Pin]

Hey
I would suggest using the substitution method.
therefore so dx = 3 du

The original equation is if you put in all the substituions you should get

which simplifies to

This should be fine to solve and then replace u with x/3 to get the final answer.