The area A of the region S that lies under the graph of the continuous function is the limit of the sum of the areas of approximating rectangles: A = lim R₂ = lim (ƒ (x1) Ax + f (x2) Ax+ ... + f (x) Ax) 11-00 72-00 (a) Use this definition to find an expression for the area under the curve y = x³ from 0 to 1 as a limit. F(;)Ki lim 812 (-)- Σ) i=1 F,()K= lim 72-0 lim 11+00 Σ i=0 n ( 3 n n (b) Use the following formula for the sum of the cubes of the first integers to evaluate the limit in part (a). 13+23+... 'n (n+1)` ²