MATH1014 Tutorial Notes02.pdf - Tutorial Notes 2(Phyllis...

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MATH1014 Calculus II (2017 Fall) Tutorial Notes 2(Phyllis LIANG) Page 1 of 6 MATH 1014 Tutorial Notes 2 Topics covered in tutorial 02: 1.Area between curves2.Volume by slicing3.Volume of revolution1. Area between curves What you need to know: • How to calculate the 3 typesof area between curves (a) Type 1: Example 2.1 Find the area of the region enclosed by the parabolas ? = ?2and ? = 2? − ?2.(b) Type 2: The area 𝐴of the region bounded by the curves ? = ?(?), ? = ?(?), and the lines ? = ?, ? = ?, where ?and ?are continuous and ?(?) ≥ ?(?)for all ?in [?, ?]is 𝑨 = ∫[?(?) − ?(?) ]????When ?(?) ≥ ?(?)for some ?, and ?(?) ≥ ?(?)for other values of ?, The area between the curves ? = ?(?)and ? = ?(?), and between the lines ? = ?and ? = ?is 𝑨 = ∫ |?(?) − ?(?)|????
MATH1014 Calculus II (2017 Fall) Tutorial Notes 2(Phyllis LIANG) Page 2 of 6 Example 2.2 Find the area of the region bounded by the curves
𝜋2. (c) Type 3: Example 2.3 Find the area enclosed by the line Some regions are best treated by regarding ?as a function of ?. If a region bounded by the curves ? = ?(?), ? = ?(?), and the lines ? = ?, ? = ?, where ?and ?are continuous and ?(?) ≥ ?(?)for all ?in [?, ?], then its area is 𝑨 = ∫[?(?) − ?(?) ]????
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