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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.
Making Equally Sized Groups : By the time children reach Class 1 or 2, they would have had many experiences of pairs of objects-pairs of shoes, pairs of eyes, ears, arms, legs, w
Decision-Making Under Conditions of Uncertainty With decision making under uncertainty, the decision maker is aware of different possible states of nature, but has insufficient
A B C play a game. If chance of their winning it in an attempt arr2/3, 1/2, 1/4 respective. A has a first chance followed by Band Called respective chances of winning the game.
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A line has the equation 2y=-3x+1. Find an equation of a line parallel to this line that has a y-intercept of -2.
Determine if the three vectors a → = (1, 4, -7), b → = (2, -1, 4) and c → = (0, -9, 18) lie in similar plane or not. Solution Thus, as we noted prior to this example al
#quesSuppose we have a stick of length L. We break it once at some point X ~ Unif(0;L). Then we break it again at some point Y ~ Unif(0;X). Use the law of iterated expectation to c
Method of cylinders or method of shells The formula for the area in all of the cases will be, A = 2 ∏ ( radius ) (heig
Use the concepts of sampling error and z- scores to explain the concept of distribution of sample means.
finding missing values from given triangle diagra m..
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