
#1
January 11th, 2015,
11:10
Have added attachment. Can anyone show me how to approach this problem? Thank you....

January 11th, 2015 11:10
# ADS
Circuit advertisement

MHB Journeyman
#2
January 11th, 2015,
14:19
Hi scottshannon!
We have $\int_1^{f(x)}g(t) \,dt =\frac{1}{3}\left(x^{3/2}8\right)$ with $f^{1}(x)=g(x)$. Applying the fundamental theorem of calculus on both sides:
$$g(f(x))\cdot f'(x)=\frac{1}{2}\sqrt{x}$$
$$x \cdot f'(x) =\frac{1}{2}\sqrt{x}$$
$$f'(x)=\frac{1}{2\sqrt{x}}$$
Solving the resulting by integrating:
$$f(x)=\sqrt{x}+C$$
Now, how may we solve for $C$?