Estimate the area under the graph, using four approximate rectangles and right endpoints.

Question

1. Estimate the area under the graph of f(x)= 1+ x² from x=-2 to x=6 using four approximate rectangles and endpoints.

2. Sketch the graph of f(x) and the four approximating rectangles.

Answer 1

Integrate ∫_-2 ⁶ (1+ x² ) dx = (x +x³/3) from -2 to 6 = 82.67

To verify,

A short cut method is by graphing the integral on a calculator the results are = 82.67