Problem

In Example 5.1.2 we showed that $ \displaystyle \…

View

Problem 42 Medium Difficulty

Given that $ \displaystyle \int^{\pi}_0 \sin ^4x \, dx = \frac{3}{8} \pi $, what is $ \displaystyle \int^0_{\pi} \sin ^4\theta \, d\theta $?

Name: given that displaystyle intpi_0 sin 4x dx frac38 pi what is displaystyle int0_pi sin 4theta dtheta
Uploaded: 2021-01-18
Duration: 1 min 38 s
Channel: Numerade
Description: Given that $ \displaystyle \int^{\pi}_0 \sin ^4x \, dx = \frac{3}{8} \pi $, what is $ \displaystyle \int^0_{\pi} \sin ^4\theta \, d\theta $?

Answer

$-\frac{3}{8} \pi$

Anna Marie V.

Campbell University

Caleb E.

Baylor University

Kristen K.

University of Michigan - Ann Arbor

Michael J.

Idaho State University

Watch More Solved Questions in Chapter 5

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

Problem 24

Problem 25

Problem 26

Problem 27

Problem 28

Problem 29

Problem 30

Problem 31

Problem 32

Problem 33

Problem 34

Problem 35

Problem 36

Problem 37

Problem 38

Problem 39

Problem 40

Problem 41

Problem 42

Problem 43

Problem 44

Problem 45

Problem 46

Problem 47

Problem 48

Problem 49

Problem 50

Problem 51

Problem 52

Problem 53

Problem 54

Problem 55

Problem 56

Problem 57

Problem 58

Problem 59

Problem 60

Problem 61

Problem 62

Problem 63

Problem 64

Problem 65

Problem 66

Problem 67

Problem 68

Problem 69

Problem 70

Problem 71

Problem 72

Problem 73

Problem 74

Problem 75

Video Transcript

given that the integral of signed to the fourth of X from zero to pi is 3/8 pie. We want to find out the exact same integral, of course, with a different variable with the limits flipped. And this is taking advantage of a property. Yeah, you'll see you over and over again and we'll jump right into it. It's just going to flip the area under the curve to become a negative when you flip the limits of integration. One way to illustrate this is if we looked at the Delta acts, for instance, but this first problem, it would end up being B minus a zero pi minus zero over and And then we could look at the turn, for instance as well. So that would end up really just simplifying too high. I over end now if we did that exact same thing with the next one, and we looked at X here we end up getting zero minus pi over and and then the I ith turned their eventually. But just in terms of the widths themselves, not ignoring even the I ith term. This one is positive. This one is negative. So that is just one demonstration of why needs values end up flipping. And when you flip the limits of integration, then it changes your answer to Ah, negative, whatever it waas.

Stephen H.

University of Utah

Related Courses

Calculus 1 / AB

Calculus: Early Transcendentals

Chapter 5

Integrals

Section 2

The Definite Integral