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Ib maths sl antiderivatives
1.
Anti-derivatives. Indefinite Integrals By the end of this lesson you will be able to: • Understand the integration process as the reverse process of differentiation. •
Calculate the integrals of powers of x and any linear combination of them.
2.
f is a function whose derivative is f '(x) = 2 x then f(x) = or f(x) = or f(x) = in general f(x) = f is the antiderivative of f '
3.
The set of all the antiderivatives of a function is called the indefinite integral of the function ∫ So: Note: Sometimes we write: F(x) to mean the integral of f(x). So we have F(x) = ∫ f(x) dx
4.
f(x) f '(x) x x2 x3 x n 1) Multiply by the power 2) Subtract 1 to the power f '(x) f(x) 1 x x2 n x 1) Add 1 to the power 2) Divide by the power
5.
In general:
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15.
The gradient function of a function H is h(x) = x +1 What is the function H? If the graph of the function H passes through (1,4), give the equation of H.
16.
A particular curve has We are told that the curve passes through the point (2, 5). Find the equation of the curve.
17.
differentiation s = displacement integration
18.
The acceleration a ms2 of a particle moving in a straight line is given by a = t +1. Find formulae for the velocity and the displacement if s =0 and v=8 when t=0.
19.
Attachments Integral=Sum.swf
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