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From: Fred Nurk on 23 Jul 2010 05:50
Find the area under the curves y = x ^ 2 and 2x + y = 15 from 0 to 15 / 2.

Why isn't this the correct sum of definite integrals?
int(15 - 2x - x ^ 2 dx, x = 0...3) + int(x ^ 2 - 15 + 2x dx, x = 3...15 /
2)?

TIA,
Albert
From: Greg Neill on 23 Jul 2010 08:10
Fred Nurk wrote:
> Find the area under the curves y = x ^ 2 and 2x + y = 15 from 0 to 15 / 2.
>
> Why isn't this the correct sum of definite integrals?
> int(15 - 2x - x ^ 2 dx, x = 0...3) + int(x ^ 2 - 15 + 2x dx, x = 3...15 /
> 2)?
>
> TIA,
> Albert

Plot the curves for the given range (on the same set of axes).
Then ask yourself what it means to find the area under the
curves.


From: Frederick Williams on 23 Jul 2010 08:13
Fred Nurk wrote:
>
> Find the area under the curves y = x ^ 2 and 2x + y = 15 from 0 to 15 / 2.
>
> Why isn't this the correct sum of definite integrals?
> int(15 - 2x - x ^ 2 dx, x = 0...3) + int(x ^ 2 - 15 + 2x dx, x = 3...15 /
> 2)?

Shouldn't the first one be a definite integral of x^2?

--
I can't go on, I'll go on.
From: Ray Vickson on 23 Jul 2010 13:10
On Jul 23, 2:50 am, Fred Nurk <albert.xtheunkno...(a)gmail.com> wrote:
> Find the area under the curves y = x ^ 2 and 2x + y = 15 from 0 to 15 / 2.
>
> Why isn't this the correct sum of definite integrals?
> int(15 - 2x - x ^ 2 dx, x = 0...3) + int(x ^ 2 - 15 + 2x dx, x = 3...15 /
> 2)?

Have you bothered to draw a picture? Over and over again you ask the
same types of questions in this forum. The answer is almost always the
same: you have failed to formulate a question correctly, probably
because you have not thought it out or visualized it correctly. Again:
the best advice is ---- DRAW A PICTURE!

R.G. Vickson

>
> TIA,
> Albert

From: Fred Nurk on 24 Jul 2010 05:29
Greg Neill wrote:
> <snip>
> Plot the curves for the given range (on the same set of axes). Then ask
> yourself what it means to find the area under the curves.

The textbook sketches http://sites.google.com/site/xtheunknown0/maths/
antidifferentiation

The line is higher than the parabola from 0 to 3 and the parabola is
higher than the line for the rest.

Fred
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