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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.
Twice a number increased by 11 is equal to 32 less than three times the number. Find out the number. Let x = the number. Now translate every part of the sentence. Twice a numb
Finding Absolute Extrema : Now it's time to see our first major application of derivatives. Specified a continuous function, f(x), on an interval [a,b] we desire to find out the
Given, y = f(x) = 2 x 3 - 3x 2 + 4x +5 a) Use the Power function to find derivative of the function. b) Find the value of the derivative at x = 4.
Every point (x,y) on the curve y=log2 3x is transferred to a new point by the following translation (x',y')=(x+m,y+n), where m and n are integers. The set of (x',y') form the curve
Question: Classify the following differential equations as linear/nonlinear. Also, what is the order of the following differential equations? Xy'-2y =x Xy'' -2y' =xsin(y)
How do you find the ratio for these problems?
two fathers and two sons went fishing . they caught only 3 fish and divided them equally among themselves without cutting. is it possible? how?
Does this Point Lie on The Line? How do you know if a point lies on a given line? For example, does the point (1, 2) lie on the line 3x + y = 7? If you graph the line and the
If 2/3 of a number is 24 then 1/4 of a number is...
use the distributive law to write each multiplication in a different way. the find the answer. 12x14 16x13 14x18 9x108 12x136 20x147
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