Pure: Integration

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Grade 1 · Term 2

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About A/L Combined Mathematics: Combined Mathematics consists of Pure Mathematics and Applied Mathematics across two years.

• Find the antiderivative of f(x) = x²: F(x) = x³/3. 2. Apply FTC: [x³/3]1² = (2³/3) - (1³/3) = (8/3) - (1/3) = 7/3. ▶ Property 1: Reversing Limits
• Split the integral: ∫0¹ x dx + ∫0¹ e^x dx
• Evaluate each part: [x²/2]0¹ + [e^x]0¹ = (1/2 - 0) + (e¹ - e⁰) = 1/2 + e - 1 = e - 1/2
• Split the integral at x=1 where |x-1| changes definition: ∫0¹ -(x-1) dx + ∫1³ (x-1) dx
• Evaluate each part:

Source: Idasara knowledge pack — english/AL_SCIENCE/combined_mathematics v13, short_notes: Lesson 08 - Reviews the basic properties of the definite integral using the Fundamental Theo

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