Find ∫(9x2−4x) dx\int \left( 9x^2 - \frac{4}{\sqrt{x}} \right) \, dx ∫(9x2−x4)dx
The gradient of a curve is given by
dydx=9x2−4x \frac{dy}{dx} = 9x^2 - \frac{4}{\sqrt{x}} dxdy=9x2−x4The curve passes through the point (9,2140)(9, 2140)(9,2140).
Find the equation of the curve.
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.