Question

Calculus help please! Find the area of the region in the first quadrant bounded by y=x(sqrt of x^2+5), the x-axis, and the line x=2

Answer 1

One of my questions is....do I use this formula? v=\[\int\limits_{a}^{b} A(x)dx ?\]

Answer 2

\(\int_0^2x\sqrt{x^2+5}\ dx\); Let \(u=x^2+5\) so \(du=2x\ dx\); substitute to yield:
\(\frac12\int_5^9\sqrt{u}\ du=\frac12[\frac23u^\frac32]_5^9=\frac13[u^\frac32]_5^9=\frac13[9^\frac32-5^\frac32]=\frac13[27-5\sqrt5]\)