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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.
Case 1: Suppose we are given expressions like 3abc and 7abc and asked to compute their sum. If this is the case we should not worry much. Because adding like exp
At the school bookstore and two binders and three pens cost $12.50. Three binders and five pens cost $19.50. What is the approximate cost of 1 binder and 1 pen? Let x = the cos
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The Limit : In the earlier section we looked at some problems & in both problems we had a function (slope in the tangent problem case & average rate of change in the rate of chan
It is totally possible that a or b could be zero and thus in 16 i the real part is zero. While the real part is zero we frequently will call the complex numbers a purely imaginar
Find the length of the second diagonal of a rhombus, whose side is 5cm and one of the diagonals is 6cm.
Randi takes the stairs at work whenever possible instead of the elevator. She must climb up 51 steps from her office to get to the accounting department. The human resources depa
Simplify following and write the answers with only positive exponents. (-10 z 2 y -4 ) 2 ( z 3 y ) -5 Solution (-10 z 2 y -4 ) 2 ( z 3 y ) -5
Solve the subsequent IVP and find the interval of validity for the solution. y' + (4/x) y = x 3 y 2 , y(2) = - 1, x > 0 Solution Thus, the first thing that we re
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