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Solve the given problems by integration.Find the area bounded by $y=3 e^{x}, x=0, y=0,$ and $x=2$.

Calculus 1 / AB

Chapter 28

Methods of Integration

Section 3

The Exponential Form

Integrals

Missouri State University

Harvey Mudd College

University of Michigan - Ann Arbor

University of Nottingham

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

00:54

Find the given area.Th…

02:26

Sketch and find the area o…

05:30

Find the area of the follo…

05:17

Find the area of the regio…

06:34

01:33

Find the area under the cu…

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Area Find the area of the …

02:45

06:19

Geometry problems Use a ta…

So we're going to find the area under the curve, Y is equal to three times E. To the X bounded by X is equal to zero, Y is equal to zero and X is equal to two. So it's bounded by the X. And Y axis is as well as X is equal to two. So this is just equal to the integral from 0 to 2 of our function three erase the power of X. Dx. So the integral um of this first thing we can do is we can take out our constant three. So this would be equal to three, multiplied by zero times two. Zero Multiplied by the integral from 0 to 2 of E to the X. D. X. And so the integral of E to the X is just E. To the X. So this would be equal to three times E. To the X. From 0 to 2. And so when X is equal to two, yeah this is equal to three times E squared. And when X is equal to zero, we have zero for just one, so this is minus three, so this will be equal to three times e squared minus one, which I'll plug into a calculator really quickly, three times He squared -1 is equal to about 19 17

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