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# C4 Integration question

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1. Looking at the 2015 paper for C4 edexcel on question 6 ii)
So I get I have to find the solution to the equation

But how does this integrate into this? The mark scheme just says its so.

2(sin^3 x)/3 ?
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2. (Original post by Dieselblue)
Looking at the 2015 paper for C4 edexcel on question 6 ii)
So I get I have to find the solution to the equation

But how does this integrate into this? The mark scheme just says its so.

2(sin^3 x)/3 ?
Done by recognition.

Follows from:

Identify f(x) and reverse the process.
3. (Original post by Dieselblue)
Looking at the 2015 paper for C4 edexcel on question 6 ii)
So I get I have to find the solution to the equation

But how does this integrate into this? The mark scheme just says its so.

2(sin^3 x)/3 ?
If you have trouble using the recognition method in the above post (like me), you can also use substitution if it makes more sense for you.

$\int 2 \sin^2y \cos{y} \ dy$

Let
$u = \sin^2y$

$\frac{du}{dy} = 2 \sin y \cos y$

$dy = \frac{1}{2 \sin y \cos y} du$

Substituting dy back into original integral

$\int \frac{2 \sin^2y \cos{y}}{2 \sin y \cos y} \ du$

$\int \sin y \ du$

$u^\frac{1}{2} = siny$

$\int u^\frac{1}{2} \ du$

$\frac{2}{3}u^{\frac{3}{2}} + C$

$\frac{2}{3}(sin^2y)^{\frac{3}{2}} + C$

$\frac{2}{3}sin^3y + C$

Obviously this method takes a lot more time than recognition, so you should probably try to learn that, but use this as a backup. Substitution can help to make complicated integrals easier, so if things aren't working out give substitution a try.
4. Alternatively you could of used the addition formulae

cos(A+B) - cos(A-B) = -2SinASinB

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