I have three questions, I don't need a full working through, but I'd prefer some hints or a simmilar example for where I am going wrong/need help. The answers arn't important, but the method of working them out is.(adsbygoogle = window.adsbygoogle || []).push({});

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1. The problem statement, all variables and given/known data

A line AB is given;

Integ{ x dy - y dx }

Where the line is the peramitised set of equations: x=t^{2}and y=t+1 between 0<t<1

2. My attempt at a solution

I've assumed that this means that I am intergrating;

Integ{ t^{2}[d/dy] - t+1 [d/dx] } dt

Which is;

Integ{ -t^{2}+2t } dt ==> 1/3 t^{3}+ t^{2}|^{1}_{0}

Therefore: 1.333...

I can't remember if this is what you do or not and considering I was going to ask some other questions I thought I'd ask this one too.

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1. The problem statement, all variables and given/known data

Knowing the double angle formula for sine(a+b). Intergrate;

Integ{ sin(2x)cos(3x) } dx

3. The attempt at a solution

My first thought was simply rearrage the double angle formula for the integrals;

Integ{ sin(5x) } dx - Integ{ cos(2x)sin(3x) } dx

But of course that gets me nowhere. Then I thought, what if I convert sin(2x) to 2sin(x)cos(x) and make my integral;

2*Integ{ sin(x)cos(x)cos(3x) } dx

But again that doesn't appear to help as I can't use a change of varible on the cos(3x) term, and if I want to expand that using the same double angle rules as before you get a nasty;

Integ{ 2sin(x)cos^{4}(x) - 2sin^{3}(x)cos^{2}(x) - 4sin^{3(x)}cos^{2}(x) }

Which I suppose is doable, but there should be a trick for this problem, and that's what I'm missing

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1. The problem statement, all variables and given/known data

Knowing d/du tan(u) = 1 + tan^{2}(u)

Intergrate;

Integ{ 1 / (1 + x^{2}) } dx

THEN find;

Integ^{Infinity}_{0}{ 1 / (3 + 2x^{2}) }

3. The attempt at a solution

For that last part I haven't a clue...

The first part however I assumed that I could let x = tan(u) and so change my integral to;

Integ{ 1 / tan(u) } du

Which using the product rule I believe intergrates to cos(u) Ln| sin(u) | + 1 as 1/tan = cos/sin

But I don't know is that's the right method as ignoring the 'hint' it gets nasty quickly :(.

Cheers and thanks in advance,

Haths

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Intergration Questions

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