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Find the area between the curves y = x and y = x^2.

Q : 2         Find the area between the curves \small y=x and \small y=x^2.

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M manish

the area between the curves \small y=x and \small y=x^2.
AOI graph
The curves intersect at A(1,1)
Draw a normal to AC to OC(x-axis)
therefore, the required area (OBAO)= area of (OCAO) - area of (OCABO)
                                                          \\=\int_{0}^{1}xdx-\int_{0}^{1}x^2dx\\ =[\frac{x^2}{2}]_0^1-[\frac{x^3}{3}]_0^1\\ =1/2-1/3\\ =\frac{1}{6}
Thus the area of shaded region is 1/6 units

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