Use the Right Endpoint method to approximate the area under...

Use the Right Endpoint method to approximate the area under the graph of the function f(x) = 3e^x over the interval [-2, 3]. Use 8 rectangles. Start by filling out the following table: i xi f(xi) f(xi)?x 1 2 3 4 5 6 7 8 3 Use the table to compute the approximate area (remember to be careful about rounding). Area ?

Transcript

00:01 So our function is 7e to the negative 2x power.

00:06 And sometimes i don't really like these types of problems because they force you to write, do a lot of work, which isn't always bad.

00:15 But what i like to do is figure out the change in x for each problem.

00:20 And so you do the upper bound minus the lower bound divided by the number of rectangles.

00:25 So we end up with six divided by six, which would be one.

00:28 So when they make that chart of, i guess, intervals, and they even say one, two, three, four, all the way down to six, i like how they tell you that at six, you better end at three.

00:44 Well, if our change in x is one, let's go backwards.

00:47 So it's two, one, you see i'm going down by one, zero, negative one, and negative two.

00:53 And what they want you to do in the next one is plug in those values in for this x.

00:57 Now i would probably just leave it as seven e to the fourth power, because negative two times negative two, and then seven e to the second power.

01:07 This next one would be seven times e to the zero.

01:10 So it would be just seven, seven e squared, seven e to the fourth, and then seven e to the sixth, sorry, negative, negative, and negative.

01:22 Now this next column is actually gonna be the same as the previous one.

01:28 So let me go ahead and just type in some decimals just to see...

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