Math 152 AU10 Exam 2 SG_0

Math 152 AU10 Exam 2 SG_0 - MSLC Math 152 Exam 2 Study...

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MSLC – Math 152 Exam 2 Study Guide 1 Topics covered since Exam 1 Section 6.2 – Volumes (basic definition, cross sections including disks/washers) Section 6.3 – Volumes using Cylindrical Shells Section 6.4 – Work (an application of integration and volumes) Section 6.5 – The Average Value of a function Section 7.1 – Integration By Parts (extremely important!) Section 7.2 – Trigonometric Integrals (dust off your identities) Section 7.3 – Trigonometric Substitutions Review: Area between two functions – 2 possible ways If we have ) ( x f y and ) ( x g y and ) ( ) ( x f x g on   b a , then use vertical slices and integrate b x a x dx x g x f ) ( ) ( . (Think right left bottom top ) If we have () x hy and x ky and ky hy for cyd then use horizontal slices and integrate yd yc hy kyd y . (Think top bottom left right ) For either method, if there is a change of function at any x or y value, you must break the integral at that point into two integrals and use the correct function on the interval VOLUMES (Sections 6.2 & 6.3, Application to 6.4 Work) While Sections 6.2 - 6.3 appear to cover three different concepts, this is not the case. All three methods – cross sections (slabs), disks/washers and shells – are all based on the same definition. b a n i i i n dx x A x x A V ) ( ) ( lim 1 where ) ( x A is a cross sectional area or “slice” and x or dx plays its usual role of thickness to give the required 3-D result. Cross-Section Method (or “slab” method) Cross sectional areas or slices can be any area we can estimate or use a geometric formula or function to describe. Typical formulas or functions would be: Squares: 2 s A 2 1 n i i Vs x  2 d x Semicircles: 2 2 1 r A 2 1 2 1 n i i Vr x 2 1 2 d x Equilateral triangles: 2 4 3 s A 2 3 4 1 n i i x 2 3 4 d x General: A Ax f x  1 n i i VA x x x d x
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This note was uploaded on 11/28/2011 for the course CHEM 121 taught by Professor Wyzlouzil during the Spring '07 term at Ohio State.

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Math 152 AU10 Exam 2 SG_0 - MSLC Math 152 Exam 2 Study...

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