Question

find the mean value theorem of f(x)=1+sqrt(x) (0,4)

Answer 1

\[\frac{1}{4}\int_0^4(1+\sqrt{x})dx=1+\frac{1}{4}\int_0^4\sqrt{x}dx\]

Answer 2

i assume you mean the "mean value of" not "the mean value theorem of" right?

Answer 3

yes

Answer 4

\[\frac{1}{4}\int_0^4\sqrt{x}dx\] should be ok by the power rule backwards. anti derivative of \(\sqrt{x}\) is \( \frac{2}{3}x^{\frac{3}{2}}\) plug in 4 and get your answer

Answer 5

btw i hope it is clear that \[\int_0^4(1+\sqrt{x})dx=\int_0^41dx+\int_0^4\sqrt{x}dx=4+\int_0^4\sqrt{x}dx\]

Answer 6

so I multiply 4 by ^(2/3)