Average function value of even and odd function, Mathematics

Assignment Help:

Average Function Value

The first application of integrals which we'll see is the average value of a function. The given fact tells us how to calculate this.

Average Function Value

The average value of function f ( x ) over the interval [a,b] is specified by,

f_avg = 1/(b-a) ∫^b_af ( x ) dx

Let's work on some quick examples.

Example Find out the average value of following functions on the specified interval.

f (t ) = t ² - 5t + 6 cos (∏, t ) on [-1, 5/2 ]

Solution

There's actually not a lot to do in this problem other than just utilizes the formula.

f _avg = 1/ ((5/2)-(-1)∫^(5/2)_(-1) t²- 5t + 6cos( ∏ t) dt|_(-1)^(5/2)

= (2/7)((1/3)t3-(5/2)t2+(6/ ∏)sin(∏ t) |_(-1)^(5/2)

= 12/7 ∏ - 13/6

= -1.620993

You caught the substitution required for the third term right?

Therefore, the average value of this function of the given interval is -1.620993.

Related Discussions:- Average function value of even and odd function

Systems of differential equations, For this point we've only looked as solv...

For this point we've only looked as solving particular differential equations. Though, many "real life" situations are governed through a system of differential equations. See the

Repetition need not be boring-ways to aid learning maths, Repetition Need N...

Repetition Need Not Be Boring : From an early age on, children engage in and learn from repetitive behaviour, such as dropping and picking up things, opening and closing boxes an

Geometry, what is the product of the solutions to the equation: x2+4x=-4

what is the product of the solutions to the equation: x2+4x=-4

Calculate the area of the skirt to the nearest foot, Pat is making a Christ...

Pat is making a Christmas tree skirt. She needs to know how much fabric to buy. Using the example provided, calculate the area of the skirt to the nearest foot. a. 37.7 ft 2

find the vector projection - vectors, Given the vectors u = 3 i - 2 j ...

Given the vectors u = 3 i - 2 j + k , v = i + 2 j - 4 k , w = -2 i + 4 j - 5 k use vector methods to answer the following: (a) Prove u , v and w can form

How much do they save if they pay the bill inside 10 days, Oscar's Oil Comp...

Oscar's Oil Company provides customers a 5% discount if they pay their bill within 10 days. The Stevens' oil bill is $178. How much do they save if they pay the bill inside 10 days

Sketch the exponental graph of f( x )=2x and g( x )= 1/2 , Example Sketc...

Example Sketch the graph of following f( x ) = 2x and g( x ) = ( 1 /2) x Solution Let's firstly make a table of values for these two functions. Following is

Determine the volume of the object, A rectangular container is 15 cm wide a...

A rectangular container is 15 cm wide and 5 cm long, and contains water to a depth of 8 cm. An object is placed in the water and the water rises 2.3 cm. Determine the volume of the

1, what''s the beneit of study mathematics ?

what''s the beneit of study mathematics ?

Derive a linear system - gauss jordan elimination, Suppose that, on a certa...

Suppose that, on a certain day, 495 passengers want to fly from Honolulu (HNL) to New York (JFK); 605 passengers want to fly from HNL to Los Angeles (LAX); and 1100 passengers want

Write Your Message!

Name

Email id

Message

Verfication Code

User Account

All Pages