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4PM1/01R Jun 2020, Question 12: Definite Integrals and Areas

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1R · Calculator · 7 marks

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The question, in short

Using the curves y = 2sin x and y = 2cos x with the shaded region R bounded by the x-axis, find point A, point B and the area of R in the form a − √b.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (a) · 1 mark

State the x coordinate where the curve y = 2cos x meets the positive x-axis.

  1. 12cos x = 0
  2. 2x = π/2

Answerπ/2

Part (b) · 2 marks

Determine the x coordinate of the intersection point of y = 2sin x and y = 2cos x lying above the x-axis.

  1. 12cos x = 2sin x
  2. 2tan x = 1
  3. 3x = π/4

Answerπ/4

Part (c) · 4 marks

By integration, work out the area of R and express it as a − √b with a and b integers.

  1. 1Area = ∫ from 0 to π/4 of 2sin x dx + ∫ from π/4 to π/2 of 2cos x dx
  2. 2= [−2cos x] from 0 to π/4 + [2sin x] from π/4 to π/2
  3. 3= (−√2 + 2) + (2 − √2)
  4. 4= 4 − 2√2 = 4 − √8

Answer4 − √8

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