A-LevelFurther MathematicsPolar coordinates9231/12 · May/June 2013 · Q14 Marks
Find the area of the region enclosed by the curve with polar equation r = 2(1 + cos θ), for 0 ≤ θ < 2π.
- (a)Find the area of the region enclosed by the curve with polar equation r = 2(1 + cos θ), for 0 ≤ θ < 2π.[4]
Mark scheme
Marking points from the official mark scheme (May/June 2013). The mark or mark type is shown in brackets.
- M1 Use of ∫½r² dθ
- A = ½ ∫₀²π 4(1 + 2 cos θ + cos² θ) dθ
- M1 Use of double angle formula and attempt to integrate.
- = ∫₀²π (3 + 4 cos θ + cos 2θ) dθ
- A1 Integrates correctly.
- = [3θ + 4sin θ + sin 2θ / 2]₀²π
- A1 Finds value.
- = 6π (CWO) Accept 18.8
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 →