This deep dive covers Integration for Exact Area (Higher) within Area Under Curves for GCSE Mathematics. Revise Area Under Curves in Graphs for GCSE Mathematics with 9 exam-style questions and 10 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 7 of 11 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 7 of 11
Practice
9 questions
Recall
10 flashcards
Integration for Exact Area (Higher)
Integration provides the exact area under a curve between two x-values (limits).
Power rule for integration: if f(x) = axⁿ, then ∫axⁿ dx = axⁿ⁺¹/(n + 1) + C
Add 1 to the power, then divide by the new power.
Example: Find the exact area under y = x² from x = 1 to x = 3.
∫₁³ x² dx = [x³/3]₁³ = (3³/3) − (1³/3) = 9 − 1/3 = 26/3 ≈ 8.67 square units
Key note: if the curve dips below the x-axis, the area calculated will be negative. To find total distance (not displacement), take the absolute value of each region and add them separately.