Easy -1.8 This is a straightforward application of basic integration with a simple fractional power. Students need only rewrite √x as x^(1/2), integrate to get (4/3)x^(3/2), and evaluate between clear limits. It's a routine textbook exercise testing only recall of integration rules with no problem-solving or conceptual challenge.
Area = integral of \(2\sqrt{x}\) attempted. → \(\frac{2x^{1.5}}{1.5}\)
B1, B1, M1, A1
Correct power of \(x\); Coefficient correct unsimplified (Value at \(x = 4\)) – (value at \(x = 1\)) co
Uses limits 1 to 4 correctly → \(\frac{32}{3} - \frac{2}{3} = 9\frac{1}{3}\) or 9.33 or \(\frac{28}{3}\)
[4]
Area = integral of $2\sqrt{x}$ attempted. → $\frac{2x^{1.5}}{1.5}$ | B1, B1, M1, A1 | Correct power of $x$; Coefficient correct unsimplified (Value at $x = 4$) – (value at $x = 1$) co
Uses limits 1 to 4 correctly → $\frac{32}{3} - \frac{2}{3} = 9\frac{1}{3}$ or 9.33 or $\frac{28}{3}$ | [4] |
2 Find the area of the region enclosed by the curve $y = 2 \sqrt { } x$, the $x$-axis and the lines $x = 1$ and $x = 4$.
\hfill \mbox{\textit{CAIE P1 2007 Q2 [4]}}