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Integration
We have, so far, seen that differential calculus measures the rate of change of functions. Differentiation is the process of finding the derivative (rate of change) of a function F(x) and is denoted by F'(x) Often, we may know the rate of change, F'(x) of a function F(x) which is unknown to us. In such situations we would like to find out the original function F(x) from the derivative, F'(x). Reversing the process of differentiation and finding out the original function from the derivative is called integration. The original function, F(x) is called the integral.
The left hand side of the equation is read as "the indefinite integral of f(x) with respect to x. The symbol is the integral sign, f(x) is the integrand and 'c' is an arbitrary constant. The arbitrary constant 'c' is added because of the following reason:
If d/dx {F(x)} = f(x) then we can also write that d/dx {F(x) + c} = f(x) where 'c' is an arbitrary constant, because the derivative of any constant is zero.
(-2x^2y4)(10xy^2)^3
A telephone company charges $.35 for the first minute of a phone call and $.15 for each additional minute of the call. Which of the subsequent represents the cost y of a phone call
A man invests rs.10400 in 6%shares at rs.104 and rs.11440 in 10.4% shares at rs.143.How much income would he get in all?
Cardioids and Limacons These can be split up into the following three cases. 1. Cardioids: r = a + a cos θ and r = a + a sin θ. These encompass a graph that is vaguel
is 49 a square number?
GIVE EXAMPLE OF ROW EQUIVALENT
Before going further, let us repeat an aspect of learning which is useful to keep in mind while formulating teaching strategies. A child who can add or subtract in the context of s
1+2+3+.....+n=1/2n(n+1)
DEVELOPING AN UNDERSTANDING OF SUBTRACTION : The process of subtraction is the reverse of that of addition. Adding more to a collection to make it bigger is just the reverse
Model of 180 meter tall building using a scale of 1.5 centimeters = 3.5 meters. How tall will the model be?
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