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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.
any example
A ?ight from Pittsburgh to Los Angeles took 5 hours and covered 3,060 miles. What was the plane's average speed? Find out the rate at that Susan is traveling through dividing h
write in factor form 9x3+9x5
(a) Find the curve on the surface z=x 3/2 joining the points(x,y,z)=(0,0,0) and (1,1,1) has the shortest arc lenght? (b) Use a computer to produce a plot showing the surface an
Compute the value of the following limit. Solution: Notice as well that I did say estimate the value of the limit. Again, we will not directly compute limits in this sec
The value of a computer is depreciated over ?ve years for tax reasons (meaning that at the end of ?ve years, the computer is worth $0). If a business paid $2,100 for a computer, ho
11% of 56 is what number?
Perpendicular to the line given by 10 y + 3x= -2 For this part we desire the line to be perpendicular to 10 y + 3x= -2 & so we know we can determine the new slope as follows,
Properties of Integration
A population forms a normal distribution with a mean of μ=80 and a standard deviation of o=15. For every samples, compute the z-score for the sample mean and determine whether the
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