Question

Evaluate \[\int_4^9\frac{\sqrt{x}}{(30-x^{\frac32})^2}\,dx.\]

Options

• \[\frac{2}{3}\]

• \[\frac{1}{22}\]

• \[\frac{1}{3}\]

• \[\frac{19}{99}\]

Answer 1

Using \(F(x)=\frac23\left[\frac{1}{30-x^{\frac32}}\right]\), evaluate \(F(9)-F(4)\).
This gives \(\frac23\left[\frac13-\frac1{22}\right]=\frac{19}{99}\).