exercise:438cb93daa: Difference between revisions
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Find the average value <math>M_a^b(f)</math> | Find the average value <math>M_a^b(f)</math> | ||
of <math>f</math> on the interval <math>[a,b]</math>, where | of <math>f</math> on the interval <math>[a,b]</math>, where | ||
<ul style{{=}}"list-style-type:lower-alpha"><li>= [0,2]</math>.</li> | <ul style{{=}}"list-style-type:lower-alpha"><li><math>f(x)=x^2-2x+1</math> and <math>[a,b]= [0,2]</math>.</li> | ||
<li><math>f(x) = 2x^3</math> and <math>[a,b] = [-1,1]</math>.</li> | <li><math>f(x) = 2x^3</math> and <math>[a,b] = [-1,1]</math>.</li> | ||
<li><math>f(x) = \frac1x</math> and <math>[a,b] = [1,2]</math>.</li> | <li><math>f(x) = \frac1x</math> and <math>[a,b] = [1,2]</math>.</li> | ||
Latest revision as of 15:16, 24 November 2024
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[/math]
Find the average value [math]M_a^b(f)[/math] of [math]f[/math] on the interval [math][a,b][/math], where
- [math]f(x)=x^2-2x+1[/math] and [math][a,b]= [0,2][/math].
- [math]f(x) = 2x^3[/math] and [math][a,b] = [-1,1][/math].
- [math]f(x) = \frac1x[/math] and [math][a,b] = [1,2][/math].
- [math]f(x) = \frac1x[/math] and [math][a,b] = [1,n][/math], where [math]n[/math] is a positive integer.
- [math]f(x) = \sin x[/math] and [math][a,b] = [0,\pi][/math].
- [math]f(x) = \ln x[/math] and [math][a,b] = [1,5][/math].