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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.
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.
Two circles touch externally. The sum of their areas is 58 π cm 2 and the distance between their centres is 10 cm. Find the radii of the two circles. (Ans:7cm, 3cm) Ans:
how to divide
Evaluate the slope of the line: Example: What is the slope of the line passing through the points (20, 85) and (30, 125)? Solution: m = 125 -85/30-20 = 4
How can i calculate arc length for dividing a circle into 10 parts
encoded with the matrix -3 -7 and 4 9. what lights up a soccer stadium? ecoded message: {-3 - 7} {3 2 } {3 6} {57 127} {52 127} {77 173} {23 51)
please suggest me that how can i get the term papers topics?
Q. What is a percentage? Ans. Percent means "per hundred", or "out of 100". A percentage can be written as a ratio, or fraction, where the denominator (bottom) is 100.
Find the Laplace transforms of the specified functions. (a) f(t) = 6e 5t + e t3 - 9 (b) g(t) = 4cos(4t) - 9sin(4t) + 2cos(10t) (c) h(t) = 3sinh(2t) + 3sin(2t)
UNDETERMINED COEFFICIENTS The way of Undetermined Coefficients for systems is pretty much the same to the second order differential equation case. The simple difference is as t
4. Two hosts, one on East (host A) and one on the west coast (host B) of the USA are exchanging data. Suppose A is sending a large file to B. The file is split into packets of size
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