Answer
$\frac{52}{3}$
Work Step by Step
Evaluate the integral: $\int^9_1 (\sqrt x) dx$
Recall the 2nd part of the Fundamental Theorem of Calculus:
$\int_a^bf(x)dx = F(b) - F(a)$
Find $F(x)$:
$F(x) =\int^9_1 (\sqrt x) dx$
$F(x) =\int^9_1 x^{\frac{1}{2} }$
$F(x) = \frac{2}{3}x^{\frac{3}{2} }$
$F(x) =\frac{2\sqrt {x}^3 }{3}$
Now evaluate $F(b) - F(a)$:
$F(9) - F(1)$
$\frac{2\sqrt {9}^3 }{3}-\frac{2\sqrt {1}^3 }{3}$
$\frac{2(27) }{3} - \frac{2}{3}$
$\frac{54}{3} -\frac{2}{3} = \frac{52}{3}$
