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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.
Related Rates : In this section we will discussed for application of implicit differentiation. For these related rates problems usually it's best to just see some problems an
If the points (5, 4) and (x, y) are equidistant from the point (4, 5), prove that x 2 + y 2 - 8x - 10y +39 = 0. Ans : AP = PB AP 2 = PB 2 (5 - 4) 2 + (4 - 5) 2 = (x
A boy covered half of distance at 20km/hr and rest at 40kmlhr. calculate his average speed.
three prices are to be distributed in a quiz contest.The value of the second prize is five sixths the value of the first prize and the value of the third prize is fourfifth that of
E1) How is the 'comparison model' different from the 'complementary addition model'? E2) Create one word problem related to the children's world for each of the 4 models liste
Reduction formulae Script for Introduction: First let us know what is meant by reduction formula. In simple words, A formula which expressess(or re
First, a solution to an equation or inequality is any number that, while plugged into the equation/inequality, will satisfy the equation/inequality. Thus, just what do we mean by
How to solve Systems of Equations ? There's a simple method that you can use to solve most of the systems of equations you'll encounter in Calculus. It's called the "substitut
Variance Square of the standard deviation is termed as variance. The semi inter-quartile range - It is a measure of dispersion which includes the use of quartile. A q
general formula of sine is Y=ysin 2(pie)x
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