![]() 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) .1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) .Let’s do some problems and set up the \(u\)-sub. (We can “trick” the integrand into having this factor.) U-Substitution Integration Problems What this says is that if we want the integral of the outside function, to make it work, we have to make sure that what we’re integrating somehow has a factor that is the derivative of the inside function. For example, for \(\displaystyle \frac\, \,C\) Why do we have to do something other than just integrate like we learned? Basically, we need U-sub to take the anti-derivative of a Composite Function it’s the “undoing” of the Chain Rule. Once you get the hang of it, it’s fun, though! U-Substitution Integration, or U-Sub Integration, is the opposite of the The Chain Rule from Differential Calculus, but it’s a little trickier since you have to set it up like a puzzle. Note that U-Substitution with Definite Integration can be found here in the Definite Integration section, U-Substitution with Exponential and Logarithmic Integration can be found in the Exponential and Logarithmic Integration section, and U-Substitution with Inverse Trig Functions can be found in the Derivatives and Integrals of Inverse Trig Functions section. Introduction to U-Substitution Which Method to Use? U-Substitution Integration Problems More Practice Tutors/Practice Sponsored Links report this ad.Applications of Integration: Area and Volume.Exponential and Logarithmic Integration. ![]() Riemann Sums and Area by Limit Definition.Differential Equations and Slope Fields.Antiderivatives and Indefinite Integration, including Trig.Derivatives and Integrals of Inverse Trig Functions.Exponential and Logarithmic Differentiation.Differentials, Linear Approximation, Error Propagation.Curve Sketching, Rolle’s Theorem, Mean Value Theorem.Implicit Differentiation and Related Rates.Equation of the Tangent Line, Rates of Change.Differential Calculus Quick Study Guide.Polar Coordinates, Equations, and Graphs.Law of Sines and Cosines, and Areas of Triangles.Linear, Angular Speeds, Area of Sectors, Length of Arcs.Conics: Circles, Parabolas, Ellipses, Hyperbolas.Graphing and Finding Roots of Polynomial Functions. ![]() Graphing Rational Functions, including Asymptotes.Rational Functions, Equations, and Inequalities.Solving Systems using Reduced Row Echelon Form.The Matrix and Solving Systems with Matrices.Advanced Functions: Compositions, Even/Odd, Extrema.Solving Radical Equations and Inequalities.Solving Absolute Value Equations and Inequalities.Imaginary (Non-Real) and Complex Numbers.Solving Quadratics, Factoring, Completing Square.Introduction to Multiplying Polynomials.Scatter Plots, Correlation, and Regression.Algebraic Functions, including Domain and Range.Systems of Linear Equations and Word Problems. ![]()
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