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# Core 3 U-Substitution Help

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1. So I have Use the substitution u = 6 - x^2

to find the value of integral sign (x^3)/sqrt(6-x^2)

The first step on the markscheme writes it out as 6-u/u^0.5

The denominator I get as it is just u to the power of a half.

But how is x^3 = 6-u?

If u= 6 - x^2

Then surely; x^2=6-u, meaning x^3 would be (6-u)^1.5?

Can someone please explain this to me?

2. (Original post by Dinasaurus)
So I have Use the substitution u = 6 - x^2

to find the value of integral sign (x^3)/sqrt(6-x^2)

The first step on the markscheme writes it out as 6-u/u^0.5

The denominator I get as it is just u to the power of a half.

But how is x^3 = 6-u?

If u= 6 - x^2

Then surely; x^2=6-u, meaning x^3 would be (6-u)^1.5?

Can someone please explain this to me?
They may have skipped to putting in du with du/dx.
3. Here is as far as I've gotten:

with limits 2 and 5.
4. Du/dx = -2x, so dx = du/-2x

Sub du/-2x in for dx. x3 cancels to x2. This is why the numerator is 6 - u

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