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Find the area of the region between the curves y=x²+x and the x-axis on the interval closed interval 1,4 using limit of riemannn sums
area under the curve is always =S(y)dx where S is the sign of integral.. hence.. area under the above curve would be =S(x²+x)dx =S(x²)dx+S(x)dx =(x^3)/3+(x^2)/2+c.... we can do the above by the formula.. S(x^n)dx ={x^(n+1)}/{n+1}..... now putting limits... we get.., =(4^3)/3+(4^2)/2-(1^3)/3-(1^2)/2 =64/3+8-1/3-1/2 =(64-1)/3+8-0.5 =21+7.5 =28.5
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