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

Theorem of reduction of order, In this theorem we identify that for a speci...

In this theorem we identify that for a specified differential equation a set of fundamental solutions will exist. Consider the differential equation y′′ + p (t ) y′ + q (t

Evaluate performance of mental arithmetic maths, E 1) Try the two activitie...

E 1) Try the two activities detailed above with a few children around you Evaluate whether they really helped to improve the children's performance of mental arithmetic. Anot

The definition of the derivative, The Definition of the Derivative : In t...

The Definition of the Derivative : In the previous section we saw that the calculation of the slope of a tangent line, the instantaneous rate of change of a function, and the ins

Obligatory application and interpretation problem, Obligatory application/i...

Obligatory application/interpretation problem : Next, we need to do our obligatory application/interpretation problem so we don't forget about them. Example : Assume that the

How to calculate percentiles, Q. How to calculate Percentiles? Ans. ...

Q. How to calculate Percentiles? Ans. In a large group of standardized test scores we expect the scores to approximate a normal curve. If all scores are translated to z-s

Solving whole number riddles, What is the answer for I am greater than 30 a...

What is the answer for I am greater than 30 and less than 40. The sum of my digits is less than 5.

Example of word problem, Example of Word problem: There is a man who i...

Example of Word problem: There is a man who is 21 years older than his son. 5 years ago he was four times as old as his son. How older are both now? Solution: Step 1

prove that 2a=b+c, If the roots of the equation (a-b) x 2 + (b-c) x+ (...

If the roots of the equation (a-b) x 2 + (b-c) x+ (c - a)= 0 are equal. Prove that 2a=b+c. Ans: (a-b) x 2 + (b-c) x+ (c - a) = 0 T.P 2a = b + c B 2 - 4AC = 0

Prove intercept of a tangent between two parallel, Prove that the intercept...

Prove that the intercept of a tangent between two parallel tangents to a circle subtends a right angle at the centre. Since Δ ADF ≅ Δ DFC ∠ADF = ∠CDF ∴ ∠ADC = 2 ∠CDF

Pi, pi to the ten-thousandths

pi to the ten-thousandths

Write Your Message!

Name

Email id

Message

Verfication Code

User Account

All Pages