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1.9 Calculus

1.9 Calculus

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Question 574

The profile of a design for a new architectural feature is defined by the region R R\,R in the xyxyxy-plane such that:

x2−7x+12≤y≤12−2x x^2 - 7x + 12 \le y \le 12 - 2x x2−7x+12≤y≤12−2x

Identify which of the following gives the area of the region RRR.

Select one box:

□∫05(x2−5x) dx\Box \int_{0}^{5} (x^2 - 5x) \, dx□∫05​(x2−5x)dx

□∫05(5x−x2) dx\Box \int_{0}^{5} (5x - x^2) \, dx□∫05​(5x−x2)dx

□∫05(x2−9x+24) dx\Box \int_{0}^{5} (x^2 - 9x + 24) \, dx□∫05​(x2−9x+24)dx

□∫(12−2x) dx−∫(x2−7x+12) dx\Box \int (12 - 2x) \, dx - \int (x^2 - 7x + 12) \, dx□∫(12−2x)dx−∫(x2−7x+12)dx

[4]
Markscheme

1.9 Calculus Questions

  1. A Level
  2. /Maths
  3. /1.9 Calculus

825 exam-style questions on OCR (MEI) A Level Maths 1.9 Calculus, covering 1.9.1 Gradient of a curve at a point, 1.9.2 Gradient as limit of chord gradient, 1.9.3 Derivative as gradient of tangent, 1.9.4 Sketch the gradient function, 1.9.5 Differentiate y = kx^n, 1.9.6 Second derivative as rate of change of gradient, 1.9.7 Stationary points: maxima and minima, 1.9.8 Increasing and decreasing functions, 1.9.9 Tangent and normal at a point, 1.9.10 Differentiate e^kx, a^kx and ln x (A-level only), 1.9.11 Differentiate trigonometric functions (A-level only), 1.9.12 Product rule (A-level only), 1.9.13 Quotient rule (A-level only), 1.9.14 Chain rule (A-level only), 1.9.15 Rates of change with the chain rule (A-level only), 1.9.16 Implicit differentiation (A-level only), 1.9.17 Concavity and the second derivative (A-level only), 1.9.18 Points of inflection (A-level only), 1.9.19 Integration as reverse of differentiation, 1.9.20 Integrate kx^n, 1.9.21 Constant of integration, 1.9.22 Indefinite and definite integrals, 1.9.23 Area between a graph and the x-axis, 1.9.24 Integrate e^kx, 1/x, sin kx, cos kx (A-level only), 1.9.25 Integration as the limit of a sum (A-level only), 1.9.26 Area between two curves (A-level only), 1.9.27 Integration by substitution (reverse chain rule) (A-level only), 1.9.28 Integration by substitution (other cases) (A-level only), 1.9.29 Integration by parts (A-level only), 1.9.30 Integration using partial fractions (A-level only), 1.9.31 Formulate first order differential equations (A-level only), 1.9.32 Solve first order differential equations (A-level only), and 1.9.33 Interpret solutions of differential equations (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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