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C4 Formula for calculating area under a curve

∫y dx/dt

When attempting to calculate the area under a curve. Do you always use the above formula? Or are there exceptions? Because I am sure I learnt a different formula in C2, just can't remember :s-smilie:

Thanks
Reply 1
Avatar for BabyMaths
BabyMaths
Most often you will need ∫ydx\int y dx
Reply 2
Avatar for EckoGecko
EckoGecko
Not sure if I've grasped what you're asking...
You use the equation of the curve you are integrating. It depends if the equation is y=3x2y=3x^2 or y=3t2y=3t^2 as to whether you use dxdx or dtdt.
Reply 3
Avatar for sabre2th1
sabre2th1
OP
12
Original post by BabyMaths
Most often you will need ∫ydx\int y dx


HOw do you know whether to apply the above formula, or the one I gave? Thanks
Reply 4
Avatar for BabyMaths
BabyMaths
Original post by sabre2th1
HOw do you know whether to apply the above formula, or the one I gave? Thanks


I think you meant ∫ydxdtdt\int y \frac{dx}{dt}dt. This is handy when you have parametric equations.
Reply 5
Avatar for james.h
james.h
11
Given a function f(x), the notation:

A=∫bcf(x) dx\displaystyle A = \int_b^c f(x)\ \text{d}x

Is more or less equivalent to saying: "A is equal to the sum of the values of f(x) over all values of x between b and c"

In other words, A is the area under the curve y = f(x) between the values x = b and x = c.

(EDIT: assuming the curve does not cross the x-axis.)
(edited 11 years ago)
Reply 6
Avatar for BabyMaths
BabyMaths
Original post by james.h


Is equivalent to saying: "A is equal to the sum of the values of f(x) over all values of x between b and c"



Kind of a dodgy definition don't you think? :tongue:
Reply 7
Avatar for james.h
james.h
11
Original post by BabyMaths
Kind of a dodgy definition don't you think? :tongue:

Implicitly assumed here are that the "function" is "nice" (continuous, piecewise finite, &c). :ninja:

...Okay, fine, but it gets the general idea across. :tongue:

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