Already have an account? Get multiple benefits of using own account!
Login in your account..!
Remember me
Don't have an account? Create your account in less than a minutes,
Forgot password? how can I recover my password now!
Enter right registered email to receive password!
The Definite Integral
If there exists an irregularly shaped curve, y = f(x) then there is no formula to find out the area under the curve between two points x = a and x = b on the horizontal axis. If this interval [a, b] is broken into 'n' subintervals [x1, x2], [x2, x3] ... [xn-1, xn] and rectangles are constructed in such a way that the height of each rectangle is equal to the smallest value of the function in the subinterval then the sum of the areas of the rectangles i.e. will approximate the actual area under the curve, where , is the difference between any two consecutive values of x. The smaller the value of the more rectangles can be created and the closer is the sum of the areas of the rectangles so formed, i.e. , to the actual area under the curve. If the number of subintervals increases, that is 'n' approaches infinity, each subinterval becomes infinitesmally small and the area under the curve can be expressed as
Figure 1
Figure 2
The area under the graph of a continuous function between two points on the horizontal axis, x = a and
x = b, can be best described by the definite integral of f(x) over the interval x = a to x = b. This is mathematically expressed as
a and b on the left hand side of the above expression are called the upper and lower limits of the integration. Unlike the indefinite integral which represents a family of functions as it includes an arbitrary constant, the definite integral is a real number which can be found out by using the =
where will we use least cost method
While we first looked at mechanical vibrations we looked at a particular mass hanging on a spring with the possibility of both a damper or/and external force acting upon the mass.
Consider the Solow growth model as given in the lecture notes using the Cobb-Douglas production function Y t = AK 1-α t L α t a) Set up the underlying nonlinear differen
Peter purchased 14 latest baseball cards for his collection. This increased the size of his collection through 35%. How many baseball cards does Peter now have? First, you must
Julie had $500. She spent 20% of it on clothes and then 25% of the remaining money on CDs. How much money did Julie spend? Find out 20% of $500 by multiplying $500 by the decim
Brian is a real estate agent. He forms a 2.5% commission on each sale. During the month of June he sold three houses. The houses sold for $153,000, $299,000, and $121,000. What was
A right triangular prism has volume equal to 288 cm^3. The height of the prism is 3 cm. One of the bases of the triangular face (not the hypotenuse) is equal to 12 cm, determine th
How can I use the I=Prt formula to get the interest for this problem? A car dealer sells me a car for $16450 with $3,290 down and $339.97 monthly payments for 48 months. What is
Rajun uses 2/3 of a carton of milk to make a pancake. The volume of milk he uses is 800ml. calculate the volume, in l, of a milk in carton?
Explain the Common Forms of Linear Equations ? An equation whose graph is a line is called a linear equation. Here are listed some special forms of linear equations. Why should
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!
whatsapp: +91-977-207-8620
Phone: +91-977-207-8620
Email: [email protected]
All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd