The areaAof the regionSthat lies under the graph of the continuous function is the limit of the sum of the areas of approximating rectangles.

A=lim R_n=lim [f(x₁)x+f(x₂)x+ . . . +f(x_n)x]

n n

Use this definition to find an expression for the area under the graph offas a limit. Do not evaluate the limit.

f(x) =3 squareroot of x, 1x14

n

A=lim = ?

n i= 1

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