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
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.