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Use the properties of integrals and the result of Example 3 to evaluate $ \displaystyle \int^3_1 (2e^x - 1) \, dx $.

$\int_{1}^{3}\left(2 e^{x}-1\right) d x=2\left(e^{3}-e-1\right) \approx 32.73$

00:46

Frank L.

00:42

Amrita B.

Calculus 1 / AB

Chapter 5

Integrals

Section 2

The Definite Integral

Integration

Campbell University

Baylor University

University of Michigan - Ann Arbor

Boston College

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

01:02

Use the result of Example …

00:57

Use a change of variables …

01:03

05:26

Use the reduction formulas…

10:10

Evaluate the integrals…

02:05

Evaluate the integrals.

02:28

Use the approaches discuss…

08:03

Use reduction formulas to …

04:40

Use the method of Example …

11:02

Yeah problem. 44. They want us to evaluate using properties of integral roles. The integral 1 to 3 to eat of the X men is one given that in a previous exercise. A few pages before this they work through an example and found this result. So properties of integral is here. This is going to be the integral from 1 to 3 of two. E to the X D x minus. The integral from 1 to 3 D X. That is to times the integral from 1 to 3. Either the X D x minus. The integral from 1 to 3 D X. Now the result that you see here, I already know that value so I can substitute that in. So this is going to be yeah, two. Mhm E cubed minus E minus. And this is just going to be three minus one. So when you do that integral is going to be So 3 -1. The reason you see this is, what does that function look like? This is like, well, one if y is equal to one from 1 to 3. Yeah, so here's one, here's one, here's three. What is the area of this rectangle? That is a one by three rectangle? Excuse me? one x 1 x two Rectangle. So it turns out this is just simply two E cubed minus E -2. Or if you factor to out of everything, EQ -E -1 is the final answer there.

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