The curve with equation y=f(x),x>0y = \mathrm{f}(x), x > 0y=f(x),x>0, passes through the point P(9,−5)P(9, -5)P(9,−5).
Given that
dydx=2xx−12x−12 \frac{\mathrm{d} y}{\mathrm{d} x} = 2x\sqrt{x} - 12x^{-\frac{1}{2}} dxdy=2xx−12x−21Find the equation of the tangent to the curve at PPP, writing your answer in the form y=mx+cy = mx + cy=mx+c, where mmm and ccc are integers to be found.
Find f(x)f(x)f(x).
438 exam-style questions on OCR A Level Maths 1.8 Integration, covering 1.8.1 Fundamental theorem of calculus (A-level only), 1.8.2 Integrating x^n, 1.8.3 Integrating standard functions (A-level only), 1.8.4 Evaluating definite integrals, 1.8.5 Area between a curve and the x-axis, 1.8.6 Area between two curves, 1.8.7 Integration as the limit of a sum (A-level only), 1.8.8 Integration by substitution (A-level only), 1.8.9 Integration by parts (A-level only), 1.8.10 Use of partial fractions in integration (A-level only), 1.8.11 Differential equations with separable variables (A-level only), 1.8.12 Interpreting the solution of a differential equation (A-level only), and 1.8 Integration. Each one has a worked solution and a mark scheme showing where the marks go.