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1.8 Integration

1.8 Integration

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Question 176
a.

Find ∫(12x2−5xx) dx\int \left( 12x^2 - \dfrac{5}{x\sqrt{x}} \right) \, dx ∫(12x2−xx​5​)dx

[3]
b.

The rate of change of the mass, MMM grams, of a chemical precipitate over time ttt minutes is modelled by the differential equation

dMdt=12t2−5tt,t>0 \dfrac{dM}{dt} = 12t^2 - \dfrac{5}{t\sqrt{t}}, \quad t > 0 dtdM​=12t2−tt​5​,t>0

Given that at t=4t = 4t=4, the mass of the precipitate is 265 grams, determine an expression for MMM in terms of ttt.

[3]
Markscheme

1.8 Integration Questions

  1. A Level
  2. /Maths
  3. /1.8 Integration

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.

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