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For example, by calculating the surface of a circle, using an integral.
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From what does pi derive from?
Pi is a number (which is 3.14....) which you will always get when you divide a circumference of circle by its diameter...
Could you find the circumference of a circle using the exact value for pi?
Yes, you could if you knew the exact value for pi as well as the diameter of the circle. Multiply the diameter by the exact value for pi to get the circumference. However, it is impossible because the exact value for pi is not known. It is only known to about a trillion decimal places, but the exact value is not known.
How determine the area of curve under the x-axis?
Integrate the function for the curve, as normal, but the change the sign of the result. Be very careful that the curve is always on the same side of the x-axis between the limits of integration. If necessary, partition the integral. For example, to find the area between the x-axis and sin(x) between x=0 and x=3*pi, you will need Integral of sin(x) between 0 and pi, -[integral of sin(x) between pi and 2*pi] - this is where the curve is below the x-axis. +integral of sin(x) between 2*pi and 3*pi.
How is pi 3.14 found?
The numerical value of pi is often found using a Taylor or Maclaurin series (Taylor series centered at 0).
What is th value of pi?
The value of pi (Ï€) is3.1415926535897932384626433832795028841971693993751.........
How will you derive the value of pi?
circumference/diameter
How will derive the value of pi?
the value of pi can be derived as the ratio between the circumference and diameter of every circle, say pi = circumference/diameter
How do you integrate periodic functions?
Same as any other function - but in the case of a definite integral, you can take advantage of the periodicity. For example, assuming that a certain function has a period of pi, and the value of the definite integral from zero to pi is 2, then the integral from zero to 2 x pi is 4.
Integral of 9 pi?
This depends on what you are integrating with respect to. Let's assume: x. Integral of 9*pi = 9*pi*x + C. However, if you are integrating with respect to pi, then integral of 9*pi is (9/2)pi^2 + C
What is the relation between definite integrals and areas?
Consider the integral of sin x over the interval from 0 to 2pi. In this interval the value of sin x rises from 0 to 1 then falls through 0 to -1 and then rises again to 0. In other words the part of the sin x function between 0 and pi is 'above' the axis and the part between pi and 2pi is 'below' the axis. The value of this integral is zero because although the areas enclosed by the parts of the function between 0 and pi and pi and 2pi are the same the integral of the latter part is negative. The point I am trying to make is that a definite integral gives the area between a function and the horizontal axis but areas below the axis are negative. The integral of sin x over the interval from 0 to pi is 2. The integral of six x over the interval from pi to 2pi is -2.
From what does pi derive from?
Pi is a number (which is 3.14....) which you will always get when you divide a circumference of circle by its diameter...
What is the integral of x sin pi x?
The method to use is 'integration by parts'; set u =x; du=dx; dv = sin(pi x)dx; v = cos(pi x)/pi. so integral(u dv) = u*v - integral(v du) then repeat the process.
What is the integral from 0 to pi over 6 sine 2x dx?
Integral from 0 to pi 6sin2xdx: integral of 6sin2xdx (-3)cos2x+c. (-3)cos(2 x pi) - (-3)cos(2 x 0) -3 - -3 0
Who worked out a value for pi using a ninety-six sided regular polygon?
Euclid discovered pi
What value is closest to the area of a circle with a 3-inch raduis explain?
There can be no "closest" value. The area is pi*r^2 Using pi = 3.14 gives the area as 28.26 sq inch Using pi = 3.14159265358979 (Excel default), gives the area as 28.2743338823081 sq inches which will be closer to the true area. The value of pi has been calculated to over 10 trillion digits and each additional digit in the value of pi gives a value for the area which is closer to the true value. . And, the value of pi can be calculated to still greater accuracy which would give a closer answer.
What is the value of pi using seven numbers to the right of the decimal?
3.1415926
How do you find the diameter of a cylinder from the area of the base?
The area of the base of a cylinder = Pi times Radius squared. Diameter of a cylinder = 2 times Pi times Radius. To find the diameter derive the area of the base by Pi and then square root the answer. That will give you the value of the radius. Multiply that answer by 2 times Pi and you will have your answer.
