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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 =
define even and odd function state whether given function are even odd or neither 1 f x =sin x cos x 2 f x {x}=x +x3n #Minimum 100 words accepted#
128sinpower8=cos8-8cos6+28cos4-56cos2+35
my daughter brought home home work im not sure how to do it the fractions has to be labled from least to greatest
Assume that Y 1 (t) and Y 2 (t) are two solutions to (1) and y 1 (t) and y 2 (t) are a fundamental set of solutions to the associated homogeneous differential equation (2) so, Y
Compare and contrast African immigrants with our immigrant groups? How are they different? What are the implications of these differences for their adjustment to the larger society
Mary made 34 copies at the local office supply store. The copies cost $0.06 each. What was the total cost of the copies? Multiply 34 by $0.06 to ?nd out the total cost; 34 × $0
6.3/o.21
11/20=
HOW TO ADD MIXED FRACTION
In a polygon no 3 diagnols are concurrent. If the total no of points of intersection are 70 ( interior ). find the no. of diagnols? Ans) Since no 3 diagonals are concurrent, There
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