Hi everyone,

Could you please tell me if this is correct?

Find the average value of the function on the given interval

g(x)=x^2sq.(1+x^3) [0,2]

1/2int. [1/3sq. u]du=

u^3/2/(9)=

.314

Thank you very much

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- Nov 15th 2007, 09:25 AMchocolateloveraverage value of a funtion
Hi everyone,

Could you please tell me if this is correct?

Find the average value of the function on the given interval

g(x)=x^2sq.(1+x^3) [0,2]

1/2int. [1/3sq. u]du=

u^3/2/(9)=

.314

Thank you very much - Nov 15th 2007, 10:17 AMticbol
average value = (Gb -Ga) / (b -a)

g(x) = (x^2)sqrt(1 +x^3), [0,2]

(Gb -Ga) = INT.(0-->2)[(1 +x^3)^(1/2)](x^2 dx)

= INT.(0-->2)[(1 +x^3)^(1/2)](x^2 dx)(3/3)

= (1/3)[(2/3)(1 +x^3)^(3/2)]|(0-->2)

= (2/9)[(1 +2^3)^(3/2) -(1 +0^3)^(3/2)]

= (2/9)[(9)^(3/2) -(1)^(3/2)]

= (2/9)[27 -1]

= 52/9

(b -a) = 2 -0 = 2

So, average value is (52/9) /2 = 26/9 = 2.889 -------answer. - Nov 16th 2007, 12:04 PMchocolatelover
Thank you very much