Problem

Find the average value of the function on the giv…

01:06

Problem 5 Easy Difficulty

Find the average value of the function on the given interval.

$ f(t) = e^{\sin t} \cos t $ , $ [0, \frac{\pi}{2}] $

Answer

$\frac{2}{\pi}(e-1)$

Topics

Applications of Integration

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 6

Applications of Integration

Section 5

Average Value of a Function

Discussion

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Watch More Solved Questions in Chapter 6

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

Video Transcript

the average value formula is one over B, which is power to minus a which is zero through zero. Power to and in our function e to the sign t course Auntie D G, which we can write out. Simplified is too over pi you to the sign two from zero to pi over too, which gives us to e months two divided by pi. So just remember one over B minus a and then the function from A to B.

Amrita B.

Topics

Applications of Integration

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 6

Applications of Integration

Section 5

Average Value of a Function

Top Calculus 2 / BC Educators

Anna Marie V.

Campbell University

Kayleah T.

Harvey Mudd College

Samuel H.

University of Nottingham

Joseph L.

Boston College