SPS SPS SM 2022 February — Question 5 6 marks

Exam BoardSPS
ModuleSPS SM (SPS SM)
Year2022
SessionFebruary
Marks6
TopicIndefinite & Definite Integrals
TypeFind curve from gradient
DifficultyEasy -1.2 This is a straightforward integration question requiring only the power rule for integration and using a given point to find the constant of integration. It's a standard textbook exercise with no problem-solving insight needed, making it easier than average but not trivial since it requires correct application of two techniques.
Spec1.08a Fundamental theorem of calculus: integration as reverse of differentiation1.08b Integrate x^n: where n != -1 and sums

The gradient of a curve is given by \(\frac{dy}{dx} = 2x^{-\frac{1}{2}}\), and the curve passes through the point \((4, 5)\). Find the equation of the curve. [6]

The gradient of a curve is given by $\frac{dy}{dx} = 2x^{-\frac{1}{2}}$, and the curve passes through the point $(4, 5)$. Find the equation of the curve. [6]

\hfill \mbox{\textit{SPS SPS SM 2022 Q5 [6]}}