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Sketch the region enclosed by the given curves. Decide whether to integrate with respect to $ x $ and $ y $. Draw a typical approximating rectangle and label its height and width. Then find the area of the region.

$ y = e^x $ , $ y = x^2 - 1 $ , $ x = -1 $ , $ x = 1 $

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$e-\frac{1}{e}+\frac{4}{3}$

Calculus 2 / BC

Chapter 6

Applications of Integration

Section 1

Areas Between Curves

Missouri State University

Harvey Mudd College

Baylor University

Boston College

Lectures

06:31

Sketch the region enclosed…

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No. Okay, so for this question, first of it all those curves Ah, so this is X y This's X axis and waxes and we draw X equals to one issues that vertical line here. And I keep Mexico's nike of one very sun in another line. And ah, for this proble X square minus one is here. And this exponential function into our axes here, right? And in the intersection here is because why you goes what on? So the shaded area will be here and ah, since everything given us represented about X, we will inter great made the respect to ex okay, interest x instead of why then we need to draw a typical approximating rectangle, Uh so probably re choose here Here is a small approximating rectangle If we scale, it probably looks something like this and the world will be out x And the height will be, um X the upper curve. Ah, riches you two the power X I miners on X lower curved excise square wireless. Okay, so this will be over typical approximating rectangle on after we read down this We know the integral is basic is based on this. So we know the shaded area of this region, eh? Now Kiko's Tio and grow ah, into the power X miners like square minus one. The ex The axe goes from negative One toe there. Now, this, uh, replying the anti dote for this that you will be in to the power X exponential. Function yourself on minus one over three X cube plus X and a battery. This one to an act of war since. Okay, so let's try this. So we know, eh? There he goes to the first one will give us no minus. Minus one third class war teaches the class to third Linus. Second one is plucking actually close to ninety war. So you two power ninety one plus here is plus one third minus one. So it's minus to third. So this will give us the finest one already. Class four, Spitter. Okay, so this will be our answer here

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