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The integral of x^5 is (1/6)x^6 + C, where C is the constant of integration.
In reimann stieltjes integral if we assume a(x) = x then it becomes reimann integral so we can say R-S integral is generalized form of reimann integral.
(that weird integral or antiderivative sign) x^(-6/5) dx =-5*x^(-1/5)
y = x2 - 5xThe integral of [ y dx ] = x3/3 - 5x2/2 + CAt x=0, the integral = 0At x=5, the integral = 125/3 - 125/2 = -20.8333At x=6, the integral = 72 - 90 = -18At x = -2, the integral = -8/3 - 10 = -12.6666a). from 0 to 5, the area is -20.8333 (20.8333 below the x-axis)b). from 0 to 6, the area is -18.c). from -2 to +5, the area is (-20.8333 + 12.6666) = +9.8333
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