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

Derivation of moment of inertia of cone revolved at x-axis, 1

Shoppers stop case study,

Combination, nc6:n-3c3=91:4

nc6:n-3c3=91:4

Reduction formulae, assinment

assinment

Proof of various limit properties, PROOF OF VARIOUS LIMIT PROPERTIES In...

PROOF OF VARIOUS LIMIT PROPERTIES In this section we are going to prove several of the fundamental facts and properties about limits which we saw previously. Before proceeding

Calculate the area of rectangle , Calculate the area of RECTANGLE ? Th...

Calculate the area of RECTANGLE ? The area of a rectangle is the amount of space taken up by a rectangle, which is a two-dimensional shape. You find the area (A) of a recta

Second order differential equation, Write the subsequent 2nd order differen...

Write the subsequent 2nd order differential equation as a system of first order, linear differential equations. 2 y′′ - 5 y′ + y = 0 y (3) = 6 y′ (3) = -1 We can wri

Negative skewness-measure of central tendency, Negative Skewness It i...

Negative Skewness It is an asymmetrical curve whether the long tail extends to the left NB: In developed countries this frequency curve for the age distribution is charact

Polynomials, On dividing p(X)=5x^(4)-4x^(3)+3x^(2)-2x+1 by g(x)=x^(2)+2 if ...

On dividing p(X)=5x^(4)-4x^(3)+3x^(2)-2x+1 by g(x)=x^(2)+2 if q(x)=ax^(2)+bx+c, find a,b and c.

Determine the general solution reduction of order, Determine the general so...

Determine the general solution to 2t 2 y'' + ty' - 3y = 0 It given that y (t) = t -1 is a solution. Solution Reduction of order needs that a solution already be iden

Write Your Message!

Name

Email id

Message

Verfication Code

User Account

All Pages