Question

If f(x) = sin(x) for all x, then the average value of f on the interval [0, π] is (A) ½ (B) 1/π (C) π/2 (D) 2/π

Answer 1

you know we have to evaluate a integral for this, right ?

Answer 2

\(\huge \int \limits_0^{\pi} \dfrac{\sin x }{(\pi-0)}dx \)

Answer 3

i have used the formula for average value over [a,b] of f(x) :
\(\huge \int \limits_a^b \dfrac{f(x)}{b-a}dx\)

Answer 4

so tell me whether you got how we formed that integral :)

Answer 5

because if you know simple integration formulas, you will be able to evaluate that integral easily.

Answer 6

@muhammadshuaib can you tell me whether you understand how i formed that integral

Answer 7

no yar i am studing fsc level..........

Answer 8

so you have not learnt integration yet ?

Answer 9

no i know about integration but not of higher level........ b/c in pak integration study not of average......in fsc level

Answer 10

solving this integral is basic level only
\(\huge \int \limits_0^{\pi} \dfrac{\sin x }{(\pi-0)}dx\)
can you solve it ?

Answer 11

i got that using the standard formula of average
f(x) = sin x
a= 0
b = pi

Answer 12

i solve it answering pi/2 are this correct

Answer 13

how did u get pi/2
can you show me steps ?

Answer 14

or was that pi/2 just a guess ?

Answer 15

-cos(x)/pi]limit
=-{cos0-cospi}/pi
=-{1-(-1)}/pi
=-2/pi

Answer 16

nice try!
but we put the upper limit first!

Answer 17

- { cos pi - cos 0}/ pi
= + 2/pi
which is your final answer :)

Answer 18

=-{cospi-coso}/pi

=-{-1-1}/pi
=-[-2]/pi
=2/pi

Answer 19

correct! good :)

Answer 20

yes ?

Answer 21

your name

Answer 22

you can call me hartnn :)

Answer 23

no i asked you only name yar.......

Answer 24

why do you need my name ?

Answer 25

my name is Muhammad shuaib pakistani
enshaALLah will chat you later
now i m going
to pray a prayer

Answer 26

nice to meet you :)
have a good day :)