Easy -1.2 This is a straightforward integration question requiring only the power rule (rewriting x^{-3} and integrating to get x^{-2}) and finding the constant using given coordinates. It's simpler than average A-level questions as it involves a single-step technique with no problem-solving or conceptual challenges.
7 The gradient of a curve is given by \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 6 } { x ^ { 3 } }\). The curve passes through \(( 1,4 )\).
Find the equation of the curve.
B3 for \((y =) -3/x^2 + c\) [B1 for each of \(k/x^2\), \(k = -6/2\) and \(+c\)] and M1 for substituting \((1, 4)\) in their attempted integration with \(+ c\), the constant of integration
5
$y = 7 - 3/x^2$ oe | B3 for $(y =) -3/x^2 + c$ [B1 for each of $k/x^2$, $k = -6/2$ and $+c$] and M1 for substituting $(1, 4)$ in their attempted integration with $+ c$, the constant of integration | 5
7 The gradient of a curve is given by $\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 6 } { x ^ { 3 } }$. The curve passes through $( 1,4 )$.\\
Find the equation of the curve.
\hfill \mbox{\textit{OCR MEI C2 2005 Q7 [5]}}