Calculus 2 Exam 1 Review Problems and Solutions

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(0:00) Trigonometric substitution integration problem
(8:46) Numerical integration and errors (empirical approach with weighted averages)
(20:10) Basic differential equation initial-value problem (just find an antiderivative)
(21:50) Differentiate an integral with variable upper limit (Fundamental Theorem of Calculus)
(26:16) Evaluate a definite integral by substitution (change the limits of integration). Could call this a u-substitution or w-substitution.
(28:37) Integration-by-parts to evaluate a definite integral
(31:27) Probability application (exponential distribution: probability density function, cumulative distribution, expected value (mean), median)
(42:13) Numerical integration approximate error analysis
(46:55) Volume of solid with semicircular cross sections and a given base
(53:33) Volume of solid of revolution (cross sections are "washers")
(59:46) Mass and center of mass of thin rod (given a linear mass density)
(1:04:45) Arc length along a parametric curve (distance traveled). Position and velocity vectors are also drawn.
(1:12:06) Comparison Test for improper integral test proof that an integral converges

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