# Talk

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(16 Posts)
albedo Tue 24-Oct-17 17:13:35

This might be a stupid question, but...

The integral of sinx is -cosx

Integration is the area under a line/curve

The area under a sine wave between 0 and pi is 2.

You see where I'm going with this. There ain't no 2 on a -cosx curve.

I'm sure my thinking is wrong somewhere. But where?

JustRichmal Tue 24-Oct-17 22:09:06

I hope someone comes along soon with the right answer, but if you add 1 as the constant of integration, does that work?

Where is Noblegiraffe when you need her?

tissuesosoft Tue 24-Oct-17 22:16:32

Is it - cos pi/2 (- cos 0) so - 0 - (-1)

tissuesosoft Tue 24-Oct-17 22:22:57

Ignore me, think I just answered a question that I didn't read properly

albedo Tue 24-Oct-17 22:28:03

Do you add a constant of integration for a definite integral?

Good lord I wish I'd paid more attention in maths

Area under sine curve between 0 and pi is (-cos (pi)) - (-cos(0)), ie you evaluate the function -cos(x) at both ends of the interval. As cos(pi) = -1 and cos(0) = 1 this area evaluates to:

-(-1) - (-1) = 1 + 1 = 2.

tissuesosoft Tue 24-Oct-17 22:36:33

The constant is not completely necessary, because it will be taken away (minus) when the integral is evaluated. But it is a good idea to keep the constant of integration.

Second curve shows the area from zero to x under the sine curve as a function of x. It is an upside-down cos curve shifted up 1, so it does indeed go to 2.

JustRichmal Tue 24-Oct-17 22:47:57

So if you integrate sine x curve which is zero when x=0, will it be -cos x +1?

If you integrate as an indefinite integral it will be -cos(x) + C.

If you want the area (definite integral) between zero and x then it will be -cos(x) - -cos(0) = -cos(x) + 1.

If you said, "the area function must take the form -cos(x) + C, and I want to measure the area from zero", then the area function must start at zero when x=0, and that leads to the same conclusion, ie that C = 1, and the area function is -cos(x) + 1.

If you wanted to measure the area between say pi/2 and x, then the answer would be different.

albedo Tue 24-Oct-17 22:55:54

So it goes from zero to two instead of -1 to 1 and they decided just to shift it down a bit?

albedo Tue 24-Oct-17 22:57:14

Ohhhhhhh yes i see what was being said about the constant of integration.

Makes sense, thank you!

OK, now come over to this thread, and join the debate about maths in schools!

JustRichmal Tue 24-Oct-17 23:18:15

albedo thanks for posting this question. Something I never thought to think about has helped trig make more sense to me.

albedo Tue 24-Oct-17 23:21:16

In all seriousness though, my grasp of basic maths is atrocious and I liked my maths lessons at school! I totally understand why people back slowly away from it with their hands over their eyes.

albedo Tue 24-Oct-17 23:23:22

@justrichmal I'm super into trig atm because of my line of work - if you've not already seen it, check out how a rotating vector makes a sine wave and how the triangles and angles come into it. So cool!

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