Area problem, Mathematics

Assignment Help:

Area Problem

Now It is time to start second kind of integral: Definite Integrals.

 The area problem is to definite integrals what tangent & rate of change problems are to derivatives.

The area problem is one of the interpretations of a definite integral and this will lead us to the definition of definite integral.

To begin we are going to suppose that we've got a function f ( x ) that is positive on some interval [a,b].  What we desire to do is find out the area of the region among the function and the x-axis.

Probably it's easiest to see how we do this with an example.  Therefore let's find out the area between f ( x ) = x2 + 1 on [0,2].  In other terms, we desire to find out the area of the shaded region below.

587_Area Problem.png

Now, at this instance, we can't do this precisely.  Though, we can estimate the area. We will estimate the area through dividing up the interval in n subintervals each of width,

                                                     Δx = (b - a)/ n

Then in each of interval we can make a rectangle whose height is specified by the function value at a particulate point in the interval.  We can then determine the area of each of these rectangles, add up them and it will be an estimate of the area.


Related Discussions:- Area problem

Simplification, 4.4238/[1.047+{1.111*[9.261/7.777]}*1.01

4.4238/[1.047+{1.111*[9.261/7.777]}*1.01

6, 200000+500

200000+500

Solving equations and/or word problems for the unknowns, With their fence i...

With their fence in place, Zack and Clint set to work landscaping yards. Since Clint did the majority of the actual landscaping and planting, he worked on the average more hours t

Mechnics, i have many trouble in this subject

i have many trouble in this subject

Determinants, can anyone solve this assigment: D=lsqrt(3x-5) sqrt(2x)l ...

can anyone solve this assigment: D=lsqrt(3x-5) sqrt(2x)l =3 l -1 1 l

Partitioning -types of word problems related to subtraction, Partitioning ...

Partitioning - an action of taking away or removing some objects, and finding out how many remain. (e.g., there were 15 toffees in this container, and 10 have been eaten. How many

Find out the length of the parametric curve, Find out the length of the par...

Find out the length of the parametric curve illustrated by the following parametric equations. x = 3sin (t) y = 3 cos (t) 0 ≤ t ≤ 2? Solution We make out that thi

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd