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1.8 Integration

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Question 26

The curve C C\,C has equation y=f(x)y = f(x)y=f(x) where x>0x > 0x>0.

Given that

  • f′(x)=(5x+2)2x2xf'(x) = \dfrac{(5\sqrt{x} + 2)^2}{x^2\sqrt{x}}f′(x)=x2x​(5x​+2)2​
  • the point P(4,−10)P(4, -10)P(4,−10) lies on CCC
a.

(i) Find the value of the gradient of the curve at PPP.

(ii) Hence find the equation of the tangent to C C\,C at PPP, giving your answer in the form ax+by+c=0ax + by + c = 0ax+by+c=0, where aaa, b b\,b and c c\,c are integers to be found.

[4]
b.

Find f(x)f(x)f(x), simplifying your answer.

[6]
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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