How to Calculate the Mean Y Value on a Curve?

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how do i calculate the mean y value on a curve?
 
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Is the function integrable? Do you know the formula for the average value of a function?
 
the curve is,

y=10/x^2

i have already found the area under the curve between two points by changing this to,

10x^-2

no i don't know the formula?
 
Last edited:
Average value of an integrable function on the closed interval [a,b] can be found via

\frac {1}{b-a} \int_{a}^{b} f(x) dx
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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