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 =
test is tomorrow, don''t know anything lol, please help
Now come to addition and subtraction of rational expressions. Following are the general formulas. (a/c) + (b/c) = (a + b)/c
what is the difference between North America''s part of the total population and Africa''s part
How do you find the slope of a straight line?
Explain Angle Theorems ? Certain angles and angle pairs have special characteristics: Vertical angles are opposite angles formed by the intersection of two lines. Vertical ang
reflection about index number in a creative way
Hello there I have question about convergence of pth root of square matrix? Do you have any expert in numerical analysis ?
classify problems in operation reseach?
Question 1 An experiment succeeds twice as often as it fails. Find the chance that in the next six trials there will be at least four successes Question 2 An insurance compan
Introduction: In this project, you will explore a few sorting algorithms. You will also test their efficiency by both timing how long a given sorting operation takes and count
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: +1-415-670-9521
Phone: +1-415-670-9521
Email: [email protected]
All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd