Values of are given at selected points

MATHEMATICS · Multi-part · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

Values of

f(x)=x^{2}

are given at selected points. x 0 0.5 2 3 f(x)\; 0 0.25 4 9 (1) Using the left endpoints of the subintervals defined by the

x

–values in the table, calculate the Riemann sum that approximates

\displaystyle\int_{0}^{3} x^{2}\,dx

. (2) The exact value of the integral is

9

. Calculate the percentage error of the approximation from part (a), rounded to the nearest tenth of a percent.