Problem

Use the properties of integrals and the result of…

01:50

Question

Answered step-by-step

Problem 43 Easy Difficulty

In Example 5.1.2 we showed that $ \displaystyle \int^1_0 x^2 \, dx = \frac{1}{3} $. Use this fact and the properties of integrals to evaluate $ \displaystyle \int^1_0 (5 - 6x^2) \, dx $.

Video Answer

Solved by verified expert

Textbook Answer

Official textbook answer

Video by Leon Druch

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

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

Okay in this problem we already know that the definite integral from 0 to 1 of x squared comes out to equal one third. Uh So we want to use that fact and properties of integral to evaluate the definite integral from 0 to 1 of to function five minus six X squared dx. Uh Well there's a couple of properties of integral that we're going to use. Uh The integral of a difference is the difference of the integral. Uh So this is going to equal the integral from 0 to 1 of five DX. Subtract The integral from 0 to 1 of ah six x squared dx. So let's rewrite integral from 0 to 1 Of five GX. Subtract Now the other property of integral is that we're about to use is the integral of a constant times of function is equal to the constant times the integral to function in other words, the integral, six x squared is really six times the integral of x squared. So we're going to take the six out of the integral sign. Um So six is now going to times the integral from 01 of x squared dx. Yeah, okay, when you integrate a constant but the definite integral of a constant is simply that constant Times uh the interval of integration we're integrating between zero and one. So the length of that integral is 1 0 or just one. So at the end of roll of five D x from 0 to 1 is just five Time to lengthen the interval 1 0 which of course will be five times one. And then we are subtracting six times the integral from 0 to 1 of x squared dx. But this was given to us in the original problem. Uh The answer is one third, so six is really just times in a value of one third, So five times 1 0, 1 0 is one. So 5 times one is 5. Subtract six times one third is to, Final answer is three.

Get More Help with this Textbook

James Stewart

Calculus: Early Transcendentals

View More Answers From This Book

Find Another Textbook

Study Groups

Study with other students and unlock Numerade solutions for free.

Problem

Use the properties of integrals and the result of…

This textbook answer is only visible when subscribed! Please subscribe to view the answer

More Answers

Related Courses

Calculus: Early Transcendentals

Related Topics

Discussion

Top Calculus 1 / AB Educators

Grace He

Kayleah Tsai

Caleb Elmore

Michael Jacobsen

Calculus 1 / AB Courses

Recommended Videos

Watch More Solved Questions in Chapter 5

Video Transcript

James Stewart

Calculus: Early Transcendentals

Grace He

Kayleah Tsai

Caleb Elmore

Michael Jacobsen

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Calculus: Early Transcendentals

Grace He

Kayleah Tsai

Caleb Elmore

Michael Jacobsen

James StewartCalculus: Early Transcendentals

Grace He

Kayleah Tsai

Caleb Elmore

Michael Jacobsen

James Stewart

Calculus: Early Transcendentals