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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.
what is cos 120
Limits At Infinity, Part I : In the earlier section we saw limits which were infinity and now it's time to take a look at limits at infinity. Through limits at infinity we mean
Logarithm Functions : Now let's briefly get the derivatives for logarithms. In this case we will have to start with the following fact regarding functions that are inverses of ea
As office manager of her firm, Marcellyne has been directed to buy new filing cabinets. She knows that cabinet A costs $10, requires 6 square feet of floor space, and holds 9 cubic
INTRODUCTION : Most of us, when planning the first mathematical experience for three-year olds, think in terms of helping them memorise numbers from 1 to 20. We also teach them to
The boundary of the shaded portion in the adjoining figure consists of our half-circles and two quarter-circles. Find the length of the boundary and the area of the shaded portion
How can I submit a sample of my work in either teaching online or checking homework as I am retired and doing this for the first time?
Dividing Whole Numbers: Example: Divide 347 by 5. Solution: Beginning from the left of the dividend, the divisor is divided into the
solve for x: logx9
Find quadratic equation using the Quadratic Formula: Solve the subsequent quadratic equation using the Quadratic Formula. 4x 2 + 2 = x 2 - 7x: Solution: Step 1.
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