0606/22 Oct/Nov 2025, Question 10: Definite Integrals and Areas
Cambridge IGCSE Additional Mathematics 0606 · Paper 22 (Calculator) · Calculator · 10 marks
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The question, in short
Find the area between y = 2 + 5eˣ and y = 4 − 3e^(2x) from their intersection to the y-axis, giving the result as a + b ln 3.
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Solution · 10 marks
- 12 + 5eˣ = 4 − 3e^(2x) gives 3e^(2x) + 5eˣ − 2 = 0
- 2(3eˣ − 1)(eˣ + 2) = 0, so eˣ = 1/3 (eˣ = −2 impossible)
- 3x = ln(1/3) = −ln 3
- 4Area = ∫ from −ln 3 to 0 of (3e^(2x) + 5eˣ − 2) dx
- 5= [(3/2)e^(2x) + 5eˣ − 2x] from −ln 3 to 0
- 6= (3/2 + 5) − (3/2 × 1/9 + 5/3 + 2 ln 3)
- 7= 14/3 − 2 ln 3
Answer14/3 − 2 ln 3
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Also searched as: 0606/22/O/N/25 · 0606_w25_qp_22 · 0606 w25 22 · question 10.
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