For example, by calculating the surface of a circle, using an integral.
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Pi is a number (which is 3.14....) which you will always get when you divide a circumference of circle by its diameter...
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.
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.
The numerical value of pi is often found using a Taylor or Maclaurin series (Taylor series centered at 0).
The value of pi (Ï€) is3.1415926535897932384626433832795028841971693993751.........