◈ Oracle PrepSign Up Free
A-LevelMathematicsIntegration9709/33 · May/June 2017 · Q44 Marks

Find the exact value of ∫(from 0 to π/2) θ sin(½θ) dθ.

  1. (a)Find the exact value of ∫(from 0 to π/2) θ sin(½θ) dθ.[4]

Mark scheme

Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.

  1. [*M1] Integrate by parts and reach aθcos(½θ) + b∫cos(½θ)dθ
  2. [A1] Complete integration and obtain indefinite integral –2θcos(½θ) + 4sin(½θ)
  3. [DM1] Substitute limits correctly, having integrated twice
  4. [A1] Obtain final answer (4–π)/√2, or exact equivalent

Write your answer and get it marked

On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.

Sign up free →

About this question

Topic
Integration, A-Level Mathematics (syllabus 9709). Structured question, 4 marks.
Source
A-Level Mathematics, May/June 2017 Paper 3 Variant 3, question 4.

Questions and mark schemes are from past examination papers and remain the copyright of the exam board. How Oracle Prep builds its content

Related Mathematics questions

IntegrationFeb/Mar 20207m

Find ∫(π/3 to π/6) x sec²x dx. Give your answer in a simplified exact form.

IntegrationFeb/Mar 20217m

A curve is such that dy 6 = and A (1, -3) lies on the curve. A point is moving along the curve dx (3x-2)3 and at A th…

IntegrationFeb/Mar 20219m

Express 5√3 cos x + 5 sin x in the form R cos(x – α), where R > 0 and 0 < α < ½π.

Numerical methodsFeb/Mar 20195m

The sequence of values given by the iterative formula x_n+1 = (2x_n^6 + 12x_n) / (3x_n^5 + 8) with initial value x₁ =…

TrigonometryFeb/Mar 20196m

Given that sin(θ + 45°) + 2 cos(θ + 60°) = 3 cos θ, find the exact value of tan θ in a form involving surds. You need…

DifferentiationFeb/Mar 20195m

The variables x and y satisfy the relation sin y = tan x, where –½π < y < ½π. Show that dy/dx = 1 / (cos x √(cos 2x)).

← Browse all past-paper questions

© 2026 Oracle Prep