# Question: a Graph the function f x e x2 2

(a) Graph the function f(x) = e –x2, – 2 < x < 2.

(b) Estimate the area under the graph of f using four approximating rectangles and taking the sample points to be

(i) Right endpoints (ii) midpoints

In each case sketch the curve and the rectangles.

(c) Improve your estimates in part (b) by using eight rectangles.

(b) Estimate the area under the graph of f using four approximating rectangles and taking the sample points to be

(i) Right endpoints (ii) midpoints

In each case sketch the curve and the rectangles.

(c) Improve your estimates in part (b) by using eight rectangles.

## Answer to relevant Questions

With a programmable calculator (or a computer), it is possible to evaluate the expressions for the sums of areas of approximating rectangles, even for large values of n, using looping. (On a TI use the Is> command or a ...Oil leaked from a tank at a rate of r(t) liters per hour. The rate decreased as time passed and values of the rate at 2-hour time intervals are shown in the table. Find lower and upper estimates for the total amount of oil ...(a) Express the area under the curve y = x5 from 0 to 2 as a limit.(b) Use a computer algebra system to find the sum in your expression from part (a).(c) Evaluate the limit in part (a).The graph of a function f is given. Estimate f(x) dx using four subintervals with (a) Right endpoints, (b) Left endpoints, and (c) Midpoints.Express the limit as a definite integral on the given interval.Post your question