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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.
A company is taking bids on four construction jobs. Three Contractors have placed bids on the jobs. Their bids (in thousands of dollars) are given in the file. (A blank indicates n
Regression line drawn as Y=C+1075x, when x was 2, and y was 239, given that y intercept was 11. calculate the residual
In a certain class, one half of the male students and two thirds of the female students speak French. If there are three fourths as many girls as boys in the class. What fraction o
Graph f ( x ) = - x 2 + 2x + 3 . Solution It is a parabola in the general form. f ( x ) = ax 2 + bx + c In this form, the x-coor
1-tan^2 A/1+tan^2 = cos A - sinA/cos A
Write down the system of differential equations for mass system and the spring above. Solution To assist us out let's first take a rapid look at a situation wherein both of
what is the circumference of a circle that is 11 in.
An integer is chosen at random from the first two hundreds digit. What is the probability that the integer chosen is divisible by 6 or 8. (Ans : 1/4 ) Ans:
Levels of significance A level of significance is a probability value which is utilized when conducting tests of hypothesis. A level of significance is mostly the probability
Formulas Now there are a couple of nice formulas which we will get useful in a couple of sections. Consider that these formulas are only true if starting at i = 1. You can, obv
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