Edexcel A2 C4 Mathematics June 2016 - Official Thread

Original post by XxKingSniprxX

Have you seen 'Good will hunting'?

YES YES YES! It's such a good movie!! :biggrin:

Reply 361

Original post by XxKingSniprxX

Omg, I remember watching 'A Brilliant Young Mind'... is that the one where he leaves the Maths exam hall running after the Chinese girl he has a crush on in the end. :biggrin:

I've got to see 'A Beautiful Mind' sometime soon....

Have you seen 'Good will hunting'?

Those three movies are incredible, and all about mathematicians which is even better :u:

Spoiler

Anyhow this isn't entirely related to C4 so we should move on, feel free to PM if you want to chat about it a bit more :biggrin:

To make this post a little more C4 related, here's a few problems:

1. Differentiate

y = x^{x}

writing your answer in terms of

x

2. What lengths does the rectangle of greatest perimeter which can be inscribed within a given circle of radius

r

have? Prove it

(edited 8 years ago)

Reply 362

Original post by Euclidean

To make this post a little more C4 related, here's a few problems:

1. Differentiate

x^{x}

writing your answer in terms of

x

Spoiler

2. What lengths does the rectangle of greatest perimeter which can be inscribed within a given circle of radius

r

have? Prove it

Spoiler

(edited 8 years ago)

Reply 363

Original post by Zacken

...

Spoiler spoiler spoiler :tongue:

(edited 8 years ago)

Reply 364

Original post by Euclidean

2. What lengths does the rectangle of greatest perimeter which can be inscribed within a given circle of radius

r

have? Prove it

As an extension: what happens if we decide to maximise the sum of the square or cube of the lengths?

Reply 365

Original post by Euclidean

Spoiler spoiler spoiler :tongue:

My apologies, spoilered! You might want to edit your quoting. :tongue:

Reply 366

Original post by Euclidean

1. Differentiate

y = x^{x}

writing your answer in terms of

x

Another extension: Differentiate

y = x^{\left(x^x\right)}

and

y = \left(x^{x}\right)^x

Reply 367

3. Using

\theta \mapsto \frac{\pi}{4} - \theta

, evaluate:

\displaystyle \int_0^{\pi/4} \ln (1 + \tan \theta) \, \mathrm{d}\theta

.

Extension: Evaluate

\displaystyle \int_0^{1} \frac{\ln (1 + x)}{1+x^2} \, \mathrm{d}x

Reply 368

Fudge2

Original post by Zacken

3. Using

\theta \mapsto \frac{\pi}{4} - \theta

, evaluate:

\displaystyle \int_0^{\pi/4} \ln (1 + \tan \theta) \, \mathrm{d}\theta

.

Extension: Evaluate

\displaystyle \int_0^{1} \frac{\ln (1 + x)}{1+x^2} \, \mathrm{d}x

Not sure what that arrow means (I'm a noob) but I assumed I could use the addition formulae stuff and got to the integral of ln(2) - ln(1+tanx) which is actually more terms than the original question....I have no idea what to do lol

(edited 8 years ago)

Reply 369

Original post by Lilly1234567890

Are we meant to know how to integrate this for c4?

Posted from TSR Mobile

Yea I think so :smile:

Original post by Lilly1234567890

How does 2sinx become (sinx+cosx)+ (sinx+cosx)

Posted from TSR Mobile

2sinx=(sinx+cosx)+(sinx-cosx)

Reply 370

Original post by Fudge2

If I say

x \mapsto f(x)

, I'm really just making a substitution

u = f(x)

then

u=x

. :-)

Well if you call your integral

I

- then you have

I = \ln 2 - I

(although that's not quite correct, use that idea).

(edited 8 years ago)

Reply 371

Original post by Zacken

As an extension: what happens if we decide to maximise the sum of the square or cube of the lengths?

Problem didn't take so long, the solution in LaTeX took a year:

Spoiler

Reply 372

Original post by Zacken

3. Using

\theta \mapsto \frac{\pi}{4} - \theta

, evaluate:

\displaystyle \int_0^{\pi/4} \ln (1 + \tan \theta) \, \mathrm{d}\theta

.

Extension: Evaluate

\displaystyle \int_0^{1} \frac{\ln (1 + x)}{1+x^2} \, \mathrm{d}x

Spoiler

Reply 373

Original post by BBeyond

Spoiler

Yep.

Reply 374

Original post by Euclidean

Problem didn't take so long, the solution in LaTeX took a year

Good work! :biggrin:

Reply 375

Original post by Euclidean

Problem didn't take so long, the solution in LaTeX took a year:

Spoiler

That is very impressive :redface:

What are you going to be doing at uni?

Reply 376

Original post by BBeyond

That is very impressive :redface:

What are you going to be doing at uni?

Maths of course! :biggrin:

Reply 377

4. Evaluate

\displaystyle \int_0^{\pi/2} \ln \sin \theta \, \mathrm{d}\theta

using a similar substitution to my other integral.

5. Generalise this substitution and prove that it holds for all smoothly behaved

f

when evaluating

\displaystyle \int_a^b f(x) \, \mathrm{d}x

(edited 8 years ago)

Reply 378

Original post by Euclidean

Maths of course! :biggrin:

Fair probs should have guessed :tongue:

Camb?

Reply 379