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

Example of inverse matrix, Determine the inverse of the following matrix, i...

Determine the inverse of the following matrix, if it exists. We first form the new matrix through tacking onto the 3 x 3 identity matrix to this matrix. It is, We

Quadratic equation assignment, what is number of quadratic equation that ar...

what is number of quadratic equation that are unchanged by squaring their roots is There are four such cases x 2 =0 root 0 (x-1) 2 =0 root 1 x(x+1)=0 roots 0 and 1

The stoichiometric reaction, Prove that a reaction following the rate law v...

Prove that a reaction following the rate law v = k[A] 2 is characterized by a linear plot of [P] t 1 versus t-l, where P is the product of the stoichiometric reaction A = P. Sho

#tnumarancyitle.., what is classification and how can you teach it?

what is classification and how can you teach it?

Topology, a couple q''s

a couple q''s

Prove that r is an equivalence relation, 1. Let S be the set of all nonzero...

1. Let S be the set of all nonzero real numbers. That is, S = R - {0}. Consider the relation R on S given by xRy iff xy > 0. (a) Prove that R is an equivalence relation on S, an

Brands, types of brands

types of brands

Obtain the equation of the diagonals, the sides of a quad taken at random ...

the sides of a quad taken at random are x+3y-7=0 x-2y-5=0 3x+2y-7=0 7x-y+17=0 obtain the equation of the diagonals

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

Determine the size of the proposed repayments, Five years ago a business bo...

Five years ago a business borrowed $100,000 agreeing to repay the principal and all accumulated interest at 8% pa compounded quarterly, 8 years from the loan date. Two years after

Write Your Message!

Name

Email id

Message

Verfication Code

User Account

All Pages