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Calculus II Study Guide

# Calculus II Study Guide - Calculus II-Fall Semester 2007...

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Calculus II-Fall Semester 2007 Riemann Sums: R=b(h 1 +h 2 +h 3 +….) Lower Riemann Sums if function is decreasing it is a right hand sum if function is increasing it is a left hand sum Upper Riemann Sums if function is decreasing it is a left hand sum if function is increasing it is a right hand sum On Calculator: ( , , , , ) ∆t sum seqft t t0 tf ∆t ex: 2xsinπx3 , =. ∆t 3 , < < 0 x 3 . ( ( , , , ,. ) 3 sum seq 2xsinπx3 0 0 3 3 ( , )≤ ( , ) L p f fxdx U p f Integrals: An integral is the area under a curve Properties of Integrals: = - ( ) abfxdx Fb F a = aafxdx 0 =- abfxdx bafxdx + = + abfx gxdx abfxdx abgxdx Area Between two Curves: - abfx gxdx Race Track Principle: If f(x) and g(x) are continuous over [a,b] and f(x)≤g(x), abfxdx abgxdx Methods for Solving Integrals: Substitution Replace a complicated x with a u Figure out the derivative of the complicated x Replace dx with the derivative of the complicated x in terms of u Trigonometric Method Replace complex x using trig identities Trig Identities + = sin2x cos2x 1 + = - cosA B cosAcosB sinAsinB = - sin2A 1 cos2A2 = + cos2A

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Calculus II Study Guide - Calculus II-Fall Semester 2007...

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