22M.1.AHL.TZ1.1

$\int \frac{3\sqrt{x}-5}{\sqrt{x}}dx=\int \left(3-5x^{-\frac{1}{2}}\right)dx$             (A1)

$\int \frac{3\sqrt{x}-5}{\sqrt{x}}dx=3x-10x^{\frac{1}{2}}\left(+c\right)$             A1A1

substituting limits into their integrated function and subtracting             (M1)

$3\left(9\right)-10{\left(9\right)}^{\frac{1}{2}}-\left(3\left(1\right)-10{\left(1\right)}^{\frac{1}{2}}\right)$  OR  $27-10\times 3-\left(3-10\right)$

$=4$             A1

 

[5 marks]

A mixed response was noted for this question. Candidates who simplified the algebraic fraction before integrating were far more successful in gaining full marks in this question. Many candidates used other valid approaches such as integration by substitution and integration by parts with varying degrees of success. A small number of candidates substituted the limits without integrating.