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...Math calculus ii lecture notes invitation only section vaughnclimenhaga contents i integration review of and the substitution rule by parts trigonometric integrals more substitutions complicated quadratics rational functions general partial fraction decompositions numerical improper applications arc length catenary surface area physical two three dimensional objects probability iii dierential equations ideas examples separable other population models linear coupled iv parametric curves polar coordinates with parametrizations geometry v sequences series date july summing an innite integral test comparison tests alternating absolute convergence ratio root power taylor maclaurin vi conic sections planetary motion parabolas ellipses hyperbolas kepler newton part stewart spivak ch denite indenite last semester we motivated introduction considering question how to determine areas this led us denitions rb f x dx is a number obtained as limit riemann sums which depends on interval can be inter...