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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.
Define A*B where: A = | 3 -3 6 | B = | 6 1 | | 0 4 2 | | 0 -5 |
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Average Function Value The average value of a function f(x) over the interval [a,b] is specified by, f avg = (1/b-a) a ∫ b f(x) dx Proof We know that the average
In the diagram points V,W,X,Y and Z are collinear, VZ=52, XZ= 20 AND WX=XY=YZ. Find the indicated length of WX, VW, WY, VX, WZ, and VY
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There are five horseracing tracks in Kentucky. The Kentucky legislature allows only one track to be open at a time. How does this restriction affect the price the track can charge
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How do you traverse a Binary Tree? Describe Preorder, Inorder and Postorder traversals with example. Ans: Traversal of tree means tree searching for a aim. The aim may be
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