Like

Report

Draw the graph of $ f(x) = \sin \left (\frac{1}{2} x^2 \right) $ in the viewing rectangle $ [0, 1] $ by $ [0, 0.5] $ and let $ I = \displaystyle \int_0^1 f(x)\ dx $.

(a) Use the graph to decide whether $ L_2 $, $ R_2 $, $ M_2 $, and $ T_2 $ underestimate or overestimate $ I $.

(b) For any value of $ n $, list the numbers $ L_n $, $ R_n $, $ M_n $, $ T_n $, and $ I $ in increasing order.

(c) Compute $ L_5 $, $ R_5 $, $ M_5 $, and $ T_5 $. From the graph, which do you think gives the best estimate of $ I $?

a. underestimate

b.$L_{n}<M_{n}<I<T_{n}<R_{n}$

Integration Techniques

You must be signed in to discuss.

a problem for Here's the grog we want to decide. How are, Um and T's, too. Let's start out to Lewis's thes Rectangle, but there's no reptile bow here. Only this truck to go So is much, much smaller than I and are ours. The whole rectangle here while he's so big and this one Yes, well, so are is greater than I. As for AM scenes the optimist car wax so we can conclude that is smaller and t he's a raft from soil Here. You can see there's our here, so t's quicker to that. So here's the ouster of part B, right in part A. Of course, our time is underestimate and t and R r overestimate. Computer five are five on fire NT five and you you need to know. Ah, 123.43 points a point. A and one. Just calculate that by is not too difficult from the graft least do you think keeps the past? Asked me if I off course is between I'm and tea. Right. So mmm. I can guess from the graph. Discuss right. Discussed. I think I'm wings, right. I just leave that have wings. I'm is better than tea. Only fast

University of Wisconsin - Madison

Integration Techniques