Riemann Sum

1. Find an approximation of the area of the region R under the graph of the function \(f\) on the interval \([−1, 2]\). Use \(n = 6\) subintervals. Choose the representative points to be the left endpoints of the subintervals.   \(\displaystyle{f(x) = 9 - x^2} \)  solution

2. Find an approximation of the area of the region R under the graph of the function \(f\) on the interval \([1, 3]\). Use \(n = 4\) subintervals. Choose the representative points to be the right endpoints of the subintervals.   \(f(x)=\frac{2}{x}\)  solution

3. Divide the interval \( [-2,3]\) into five subintervals of equal length. Then approximate the area under the curve \(y=f(x)\) on \( [-2,3]\) sketching the corresponding rectangles using left endpoints of each subinterval. Repeat this using right end points of each subinterval.  solution

graph1

4. Divide the interval \( [0,4]\) into four subintervals of equal length. Then approximate the area under the curve \(f(x)=\sqrt{x}\) on \( [0, 4]\) sketching the corresponding rectangles using right-end points.  solution

graph2