[karate_kat]

I'm just revising for C4 tomorrow, and can't do a couple of these qus, so any help would be appreciated, thanks

1. Find the integral of x*(x^2+3)^5 dx

2. Find the integral of (sinx)^2 * cosx dx

[aster100]

Originally Posted by karate_kat

I'm just revising for C4 tomorrow, and can't do a couple of these qus, so any help would be appreciated, thanks

1. Find the integral of x*(x^2+3)^5 dx

2. Find the integral of (sinx)^2 * cosx dx

simple sub and derivative;

1. 1/12 (x^2 + 3)^6
2. - 1/3 (sinx)^3

[montyr]

The first one is pretty simple...hint x^2 differentiates to 2x...

The second one change sin^2x for 1/2 - cos2x/2

[Adje]

For both of them, make a substitution of the bracketed function, i.e. and .

[montyr]

Altho doing that on the second one i've got stuck lol!

I've ended up with cosx/2 +cos2xcosx/2

Just realised what I'm doing wrong! Although I then get sin^3(x) all divided by 3...where does the minus come from?

[karate_kat]

Ok, I've done the 1st one, and I've got it right. At first I thought I was supposed to do integration by parts and not substitution.
Usually in the exam they tell you what to substitute in, but the book doesn't.
Onto the 2nd one now.

[karate_kat]

I've done the 2nd one as well, again I tried integration by parts, and substitution but with u = cosx, which made it a bit more complicated.
Thanks guys

[aster100]

Originally Posted by montyr

Altho doing that on the second one i've got stuck lol!

I've ended up with cosx/2 +cos2xcosx/2

Just realised what I'm doing wrong! Although I then get sin^3(x) all divided by 3...where does the minus come from?

do u = sin x
then dx / du = -1/cosx

so the integral is transformed to - int (u^2) = - 1/3 u ^3 = -1/3 sin ^3 x

[montyr]

But isn't sin differentiated cos? and cos differentiated is -sin?

so dx/du would be secx?

[karate_kat]

Yeh, the answers positive.

[aster100]

Originally Posted by montyr

But isn't sin differentiated cos? and cos differentiated is -sin?

so dx/du would be secx?

Correct

lol sorry I'm getting confused

the answer would be as you said 1/3u^3

[montyr]

Originally Posted by aster100

Correct

lol sorry I'm getting confused

the answer would be as you said 1/3u^3

I wasn't sure if it was me getting confused lol! Having to remember both the integration and differentiation formulae does get confusing!!

[Goldenratio]

Originally Posted by karate_kat

I'm just revising for C4 tomorrow, and can't do a couple of these qus, so any help would be appreciated, thanks

1. Find the integral of x*(x^2+3)^5 dx

2. Find the integral of (sinx)^2 * cosx dx

These are both of the type:

ie you can recognise these integrands easily by just seeing what the integrand looks like differentiated and comparing the coefficients. yeah?

eg differentiate which is just a complicated version of what you have in 2.