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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 sphere and a cube have equal surface areas. Show that the ratio of the volume of the sphere to that of the cube is √6 : √π. Ans: S.A. of sphere = S.A of cube 4π r 2
INTRODUCTION : We are often confronted with children not being able to deal with H T 0, i.e. 'hundreds', 'tens' and 'ones' (or 'units'), with comfort, though they are supposed to
The width of a rectangle is 30.5% of its length l. Write a formula for the area and perimeter of the rectangle in terms of l only
Easy Rider taxi service charges a pick-up fee of $2 and $1.25 for each mile. Luxury Limo taxi service charges a pick-up fee of $3.25 and $1 per mile. How many miles required to be
How will you find the vertex of a parabola given in 2nd degree form (the axis of parabola is not parallel to coordinate axes)? Ans) Write the equation in type of standard form.
The diagram below shows the cross section of a pipe 1/2 inch thick that has an inside diameter of 3 inches. Determine the area of the shaded region in terms of π. a. 8.75π i
If you find nothing out of this rapid review of linear algebra you should get this section. Without this section you will not be capable to do any of the differential equations wo
It may seem like an odd question to ask and until now the answer is not all the time yes. Just as we identify that a solution to a differential equations exists does not implies th
Integration We have, so far, seen that differential calculus measures the rate of change of functions. Differentiation is the process of finding the derivative
I need to follow the pattern .125,.25,.375,.5, ?
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