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# Core Maths 3: How do you integrate this?

1. 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
2. The integral of sin(ax+b) is -(1/a)cos(ax+b).
That means in this situation a is 1/3.
3. ok so in my case its -3 cos x ??
4. The x value must remain the same as 'a' remains in front it.
5. so its -3 cos 1/3x which is - cos x??
6. 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
7. ok thank you very much
8. (Original post by jackie11)
ok thank you very much
No problem; thanks for the rep.
9. 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.

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