Question

find the average values of function over the corresponding intervals 1/x on [1,4]

Answer 1

please ????

Answer 2

\(\dfrac{\int\limits_{1}^{4}\dfrac{1}{x}\; dx}{4-1}\)

Are we ringing bells? Think about a rectangle, but shred the top a little.

Answer 3

i don't know please tell me

Answer 4

average value is integral divided by the length of the path
what @tkhunny said
\[\frac{1}{3}\int_1^4\frac{1}{x}dx\]

Answer 5

anti derivative of \(\frac{1}{x}\) is \(\ln(x)\) so you get
\[\frac{1}{3}\left(\ln(4)-\ln(1)\right)\]

Answer 6

i know the formula for the average but i don't know who i use it in ihis equation

Answer 7

since \(\ln(1)=0\) this is \(\frac{1}{3}\ln(4)\)

Answer 8

1/3 write

Answer 9

please must to solve it by the law (1/b-a)integration fx dx

Answer 10

so how i start to solve

Answer 11

i wrote the complete solution above

Answer 12

thank you