Area Under Curves and Volume of Revolving a Curve Discussions | Functional Programming | HackerRank
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Area Under a Curve:
[
A = \int_{a}^{b} f(x) ,dx
]
It represents the integral of a function ( f(x) ) over an interval ([a, b]), giving the total area between the curve and the x-axis.
Volume of Revolution (about x-axis):
[
V = \pi \int_{a}^{b} [f(x)]^2 ,dx
]
This integral computes the volume of the solid formed by rotating ( f(x) ) around the x-axis.
Area Under Curves and Volume of Revolving a Curve
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Area Under a Curve:
[ A = \int_{a}^{b} f(x) ,dx ]
It represents the integral of a function ( f(x) ) over an interval ([a, b]), giving the total area between the curve and the x-axis.
Volume of Revolution (about x-axis):
[ V = \pi \int_{a}^{b} [f(x)]^2 ,dx ]
This integral computes the volume of the solid formed by rotating ( f(x) ) around the x-axis.
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