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Q52Section C (Section C)52 of 60

Area between a cubic and the line y=x

Let f:R→Rf:\mathbb{R}\to\mathbb{R} and g:R→Rg:\mathbb{R}\to\mathbb{R} be given by f(x)=x3+2x2−15xf(x)=x^3+2x^2-15x and g(x)=xg(x)=x respectively. Let x0x_0 be the smallest strictly positive number such that f(x0)=0f(x_0)=0. Then the area of the region enclosed by the graphs of ff and gg between the lines x=0x=0 and x=x0x=x_0 is __________ (round off to 2 decimal places)

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