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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.
Solve the following Linear Programming Problem using Simple method. Maximize Z= 3x 1 + 2X 2 Subject to the constraints: X 1 + X 2 ≤ 4
castor brought 6 3/4 carat cakes to share with 26 students. did castor bring enough for each student to have 1/4 of cake?
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Smooth Curve - Three Dimensional Space A smooth curve is a curve for which → r' (t) is continuous and → r' (t) ≠ 0 for any t except probably at the endpoints. A helix is a s
x 4 - 25 There is no greatest common factor here. Though, notice that it is the difference of two perfect squares. x 4 - 25 = ( x 2 ) 2 - (5) 2 Thus, we can employ
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