Easy -1.3 This is a straightforward integration question requiring only direct application of the power rule and use of a boundary condition to find the constant. It's simpler than average A-level questions as it involves no chain rule, substitution, or problem-solving—just routine integration and substitution of a point.
1 A curve is such that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = 2 x ^ { 2 } - 5\). Given that the point \(( 3,8 )\) lies on the curve, find the equation of the curve.
1 A curve is such that $\frac { \mathrm { d } y } { \mathrm {~d} x } = 2 x ^ { 2 } - 5$. Given that the point $( 3,8 )$ lies on the curve, find the equation of the curve.
\hfill \mbox{\textit{CAIE P1 2005 Q1 [4]}}