Problem

Evaluate the integral. $ \displaystyle \int_1^…

02:05

Problem 17 Easy Difficulty

Evaluate the integral.

$ \displaystyle \int_0^\pi t \cos^2 t\ dt $

Answer

$$\frac{1}{4} \pi^{2}$$

Topics

Integration Techniques

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 7

Techniques of Integration

Section 5

Strategy for Integration

Discussion

You must be signed in to discuss.

Top Calculus 2 / BC Educators

Grace H.

Anna Marie V.

Campbell University

Kayleah T.

Harvey Mudd College

Joseph L.

Boston College

Watch More Solved Questions in Chapter 7

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

Problem 76

Problem 77

Problem 78

Problem 79

Problem 80

Problem 81

Problem 82

Problem 83

Problem 84

Video Transcript

Let's evaluate this in a girl by using the integration by parts. Let's take unit B t Do you equals DT? Then we're left over with DV equals coastlines flair DT But here to find me we will have to do a little bit of work. You have to integrate co science where? Just use the half angle identity Here this is one plus coz I into t all divided by two Pull up the one half So here we have tea over to and then sign two tea over for if there's two teas bothering you, you could do a use up here and no need to add the constant in a veneration here because well, either it in at the very end. So now recall the formula integration by parts for a definite in a roll. So plugging in are you and B we have t square over too. If he signs of Tootie over four zero pie, that's two you times me and then minus in a girl syrup. I t over too Scientist t over for So let's just go ahead and evaluate this first expression over here by plugging in pie first and then zero So there you end up with Paice. Where Over too After simple Fine. And then over here for the Southern girl. So here that he So let's actually pull of the minus Then we'LL integrate So this will also change using the power rules he square over for And then this is we'll have co sign of two t over eight zero pie and then here this will be a minus So hear this minus turns this into a minus and the integral of minus sign is co sign positive Go sign. And that's exactly what we have here after this double minus. So go ahead and plug in pi and zero in for tea and we'Ll end up with Thais clear over four in this equals Pi ce were over for And that's our answer

JH

J H.

Topics

Integration Techniques

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 7

Techniques of Integration

Section 5

Strategy for Integration

Top Calculus 2 / BC Educators

Grace H.

Numerade Educator

Anna Marie V.

Campbell University

Kayleah T.

Harvey Mudd College

Joseph L.

Boston College