Basic Integral Question

[Aus.copper]

Hi everyone,

I have attached an image regarding my question. My question pertains to obtaining the denominator in the result.

f) I simply use 'a/(b/c)' and get '1/3' from 1/6 * 1/(1/2). Which satisfies the answer.

g) I again use 'a/(b/c)' and get '4/10' from 1/10 * 1/(1/4). Which does not satisfy the answer of having 40 in the denominator.

It seems I'm missing something quite simple, but I can't spot it.

Thank you very much

 

[Aus.copper]

Wow. I think I've just realized... After writing all of this neatly, taking a photo and uploading and getting away from the pen.

Because the exponent in f) is sqrt or ^-(1/2) ... AKA a fuction. Hence 1/(1/2)

Where as the exponent in g) is just a number. Hence 1/4

Is this correct?

 

[Steven G]

for f: You computed du incorrectly.

for g: why are you dividing by 1/4??

 

[pka]

I would start by looking at derivatives.
\(\large D_x\left(\sqrt{6x-2}\right)=\dfrac{6}{2\sqrt{6x-2}}\)

\(\large D_x\left(x^{10}+1\right)^4=4\left(x^{10}+1\right)^3\left(10x^9\right)\)