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Maths C2

What does evaluating a integral do, why is it done?

thanks
Reply 1
Avatar for Zacken
Zacken
22
Moved to maths.
Original post by Lord1
What does evaluating a integral do, why is it done?

thanks


Imagine splitting the region beneath the curve into a infinite series of trapezia and then summing up the areas of all these trapezia. That is essentially what, when you integrate, you get an expression for. When you substitute two values into that, you then get the area of all those trapezia between those two points.

That is why we must use two points because it would not make sense to have an area at a point - area is always between things.

It's quite useful in a number of situations, i.e. working out the charge from a current-time graph when current and time do not follow a linear relationship, working out the displacement travelled by an object from a velocity-time graph and so on.
(edited 8 years ago)
Reply 3
Avatar for Zacken
Zacken
22
Original post by kingaaran
Imagine splitting the region beneath the curve into a infinite series of trapezia and then summing up the areas of all these trapezia. T


Rectangles, not trapezia. :-)
Original post by Lord1
What does evaluating a integral do, why is it done?

thanks


It's the exact opposite of differentiation, it's usually done to find the area under a specific section of a curve.
Original post by Zacken
Rectangles, not trapezia. :-)


Ah, my bad.
area beneath a curve is the main use.

also finding volumes of revolution ?
the definite integral is a generalization of a Rieman summation; the integral sign is meant to be a weird 'S' which stands for 'summation'. A Riemann summation finds the area under an infinite amount of infinitesimal small rectangles under a curve. https://en.wikipedia.org/wiki/Riemann_sum

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