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integration watch

1. I don't know how to do this.

I get that answers but there's a minus in front! I thought when u integrate sin u get -cos

could someone please go through the steps? thankyou.
2. let u = sin t => du = cos t dt

then ∫u5 du
3. (Original post by FoOtYdUdE)

I don't know how to do this.

I get that answers but there's a minus in front! I thought when u integrate sin u get -cos

could someone please go through the steps? thankyou.
Yes, this is correct.

Do you use the "trig wheel"? I always use it, as silly as it looks...and it works great!

___S

-C____C

___-S

It's like a wheel, see? (sorry my 'art' is so awful - but bear with me!)

S means sin, C means cos. Start from, say, S...if you differentate you go down (clockwise), to get cos. Differentiate cos and you get -sin...etc.

If instead you wanted to integrate and start with, say, -cos...you integrate and you get -sin (going anti-clockwise now), integrate again and get cos...

I'm a 2nd year physics student (at university) and I still use this method to do calculus with trig functions. I just scribble it in the margin and I never get confused. Try it out!

EierVonSatan's method was, predictably, completely correct, by the way .
4. (Original post by M_E_X)
Yes, this is correct.

Do you use the "trig wheel"? I always use it, as silly as it looks...and it works great!

___S

-C____C

___-S

It's like a wheel, see? (sorry my 'art' is so awful - but bear with me!)

S means sin, C means cos. Start from, say, S...if you differentate you go down (clockwise), to get cos. Differentiate cos and you get -sin...etc.

If instead you wanted to integrate and start with, say, -cos...you integrate and you get -sin (going anti-clockwise now), integrate again and get cos...

I'm a 2nd year physics student (at university) and I still use this method to do calculus with trig functions. I just scribble it in the margin and I never get confused. Try it out!

EierVonSatan's method was, predictably, completely correct, by the way .
Awww, beautifully explained.
5. (Original post by EierVonSatan)
let u = sin t => du = cos t dt

then ∫u5 du
Brilliant!

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