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).
Practise AQA A Level Maths 1.11 H: Integration with exam-style questions for A Level Maths. 436 questions covering 1.11.1 Fundamental Theorem of Calculus, 1.11.2 Integrating standard functions, 1.11.3 Definite integrals and areas, 1.11.4 Integration as the limit of a sum (A-level only), 1.11.5 Integration by substitution and by parts (A-level only), 1.11.6 Integration using partial fractions (A-level only), 1.11.7 Differential equations with separable variables (A-level only), and 1.11.8 Interpreting solutions of differential equations (A-level only), matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
