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Find the area bounded by the curve y = 4 – x2 and the lined y = 0, y = 3.
The given equations are,
Y = 4 – x2 ...(i)
Y = 0 ...(ii)
And y = 3 ...(iii)
Equation (i) represents a parabola with vertex (0,4) and passes through (0,2),(0,02)
Equation (ii) is x - axis and cutting the parabola at C (2, 0)and D( – 2,0)
Equation (iii) is a line parallel to x - axis cutting the parabola at A(3,1)and B( – 3,1)
On solving these equations, we get point of intersections.
The points of intersections of a parabola with the other two lines are A(3,1), B( – 3,1), C(2,0) and D( – 2,0). These are shown in the graph below
Now the bounded area is the required area to be calculated,
Hence, Bounded Area, A = 2 times [Area between the equation (i) and y axis from y = 0 to y = 3]
On integrating the above definite integration,
The area bounded by the curve y = 4 – x2 and the lined y = 0, y = 3 is .