Application of Integrals

The elementary area is the area which is located at an arbitrary position within the region which is specified by some value of x between a and b. Consider the area bounded by the curve y = f (x), x-axis and the ordinates x = a and x = b. The area bounded by simple curves and the axes can be calculated using a vertical strip and using a horizontal strip. While using a vertical strip, the area is enclosed between the curve y = f(x), lines x = a, x = b and x - axis. The formula of area is given by the definite integral of the function f(x), w.r.t x, from the closed interval ‘a’ to ‘b’. While using a horizontal strip, the area is enclosed between the curve y = f(y), lines y = a, y = b and y - axis. The formula of area is given by the definite integral of the function g(y), w.r.t y, from the closed interval ‘c’ to ‘d’. If the position of the curve under consideration is below the x-axis, then we should take the numerical value of the area. The area between two curves is given by the definite integral of the difference of two functions, f(x) and g(x), w.r.t. x, from the closed interval ‘a’ to ‘b’ and here we take the positive or modulus of definite integral. Keywords: Curve, Definite integral

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