C4 Edexcel hardest questions

Original post by Khallil

\displaystyle \int \sec^3 x \text{ d}x

Very nice! I always like the ones where you use IBP and end up adding the integral to the other side and dividing. :colone:

(edited 10 years ago)

Reply 5

Original post by majmuh24

Very nice! I always like the ones where you use IBP and end up adding the integral to the other side and dividing. :colone:

I used a substitution :colone:

was doing it late at night though so now I need to evaluate my integral in terms of u

Reply 6

Original post by Robbie242

I used a substitution :colone:

was doing it late at night though so now I need to evaluate my integral in terms of u

Hmm, I've never been a fan of trig substitutions unless absolutely necessary. Did you use the tangent half angle sub (also known as the Weierstrass sub) by any chance?

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Reply 7

Original post by majmuh24

Hmm, I've never been a fan of trig substitutions unless absolutely necessary. Did you use the tangent half angle sub (also known as the Weierstrass sub) by any chance?

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Nah I'm a noob, I did a u=tanx substiution and got my integral down to

I=\displaystyle\int (1+u^{2})^{\frac{1}{2}} du

but struggling to evaluate this xD

Reply 8

Original post by Robbie242

Nah I'm a noob, I did a u=tanx substiution and got my integral down to

I=\displaystyle\int (1+u^{2})^{\frac{1}{2}} du

but struggling to evaluate this xD

Try it the IBP way by splitting it up and use some trig identities, I think you've overcomplicated it. You could cheat and use a reduction formula, but that's not C4 stuff (and it involves the IBP method anyway :tongue:

)

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Reply 9

Original post by majmuh24

Try it the IBP way by splitting it up and use some trig identities, I think you've overcomplicated it. You could cheat and use a reduction formula, but that's not C4 stuff (and it involves the IBP method anyway :tongue:

)

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I think I have, checked wolfram alpha and then started using hyperbolic sin in their answer haha! I'll try IBP thanks

Reply 10

Original post by Robbie242

I think I have, checked wolfram alpha and then started using hyperbolic sin in their answer haha! I'll try IBP thanks

I think that involves some Pythagoras and reduction formulae for hyperbolic functions as well, so maybe not the way to go :s-smilie:

Reply 11

Original post by majmuh24

I think that involves some Pythagoras and reduction formulae for hyperbolic functions as well, so maybe not the way to go :s-smilie:

Haha I did it by IBP

I got this

Spoiler

Reply 12

Original post by Robbie242

Haha I did it by IBP

I got this

Spoiler

Yep, looks good! :thumbsup:

Reply 13

Evaluate the integral
\displaystyle\int x^3 \sqrt{1-x^2}

If you want a hint, PM/quote me. :smile:

Reply 14

Glavespian

Original post by majmuh24

Evaluate the integral
\displaystyle\int x^3 \sqrt{1-x^2}

If you want a hint, PM/quote me. :smile:

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Thanks, this one was rather fun. I went down a dead end at first, but a different path proved successful, not as hard as sec^3 x though.

Spoiler

Where do you get these from though? They're a nice challenge. :smile:

Reply 15