Application of Integrals

  • We can use integrals to find the area bounded by a curve and a line and area bounded by two curves.
  • 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 x = g(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’.
  • 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: Area between the curves, Area between a curve and a line.

 

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  • Q1

    Area between the curve y = 4 + 3x - x2 and x-axis in square units is

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  • Q2

    The area enclosed by the curve x2y = 36, the x-axis and the lines x = 6 and x = 9 is

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    2.

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  • Q3

    The area of the region bounded by the curves y = |x - 1| and 3 - |x| is

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    4.

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  • Q4

    If A is the area lying between the curve y = sinx and x-axis between x = 0 and x = /2. Area of the region between the curve y = sin2x and x-axis in the same interval is given by

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    A.

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  • Q5

    Area of the region bounded by the line x – y + 2 = 0 , y-axis and the curve is

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