Homework Soursefind the area of the region enclosed by i y x31 ii y x1 iii
find the area of the region enclosed by
i) y= x^3-1
ii) y= x-1
iii) to the right of the y axis
i) y= x^3-1
ii) y= x-1
iii) to the right of the y axis
Solution
area enclosed = integral from x = 0 to x= 1 {(x^3-1)-(x-1) }dx integral (-x+x^3) dx Integrate the sum term by term and factor out constants: = integral x^3 dx- integral x dx The integral of x is x^2/2: = integral x^3 dx-x^2/2 The integral of x^3 is x^4/4: = x^4/4-x^2/2+constant answer =1/4
