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Work Problems - Calculus

Work Problems - Calculus

This calculus video tutorial explains how to solve work problems.  It explains how to calculate the work required to lift an object against gravity or the work required to push a car with a constant force to a certain displacement.  This video also explains how to calculate the work done by a variable using calculus.  The definite integral of a force function with respect to x is...

Integration By Parts

This calculus video tutorial provides a basic introduction into integration by parts.  It explains how to use integration by parts to find the indefinite integral of exponential functions, natural log functions and trigonometric functions.  This video contains plenty of examples and practice problems.

Trigonometric Integrals

This calculus video tutorial provides a basic introduction into trigonometric integrals.  It explains what to do in order to integrate trig functions with even  powers and how to employ u-substitution integration techniques and power reducing formulas in order to find the indefinite integral of trig functions with sin, cos, tan, and sec.  This video contains plenty of examples an...

Trigonometric Substitution

This calculus video tutorial provides a basic introduction into trigonometric substitution.  It explains when to substitute x with sin, cos, or sec.  It also explains how to perform a change of variables using u-substitution integration techniques and how to use right triangle trigonometry with sohcahtoa to convert back from angles in the form of theta to an x variable.  There's ...

Integration By Partial Fractions

This calculus video tutorial provides a basic introduction into integrating rational functions using the partial fraction decomposition method.  Partial fraction decomposition is the process of breaking a single complex fraction into multiple simpler fractions.  The integrals of many rational functions lead to a natural log function with absolute value expressions.  This video ex...

Improper Integrals - Convergence and Divergence

This calculus 2 video tutorial explains how to evaluate improper integrals.  It explains how to determine if the integral is convergent or divergent by expressing the limit as it approaches infinity.  It also explains how to determine if the integral is improper by identifying any vertical asymptotes or infinite discontinuites.  This video contains plenty of examples and practice...

Integration Into Inverse Trigonometric Functions Using Substitution

This calculus video tutorial focuses on integration of inverse trigonometric functions using formulas and equations.  Examples include techniques such as integrating by substitution, u-substitution, splitting fractions and completing the square.  This video  contains plenty of practice problems of integrating inverse trig functions.

Integration of Rational Functions Into Logarithms By Substitution & Long Division

This calculus video tutorial focuses on the integration of rational functions that yield logarithmic functions such as natural logs.  The techniques involve include integrating by substitution, long division, and splitting a fraction into multiple smaller fractions all of which will produce natural logarithms containing absolute value functions.  This video contains plenty of examples...

Integral of Logarithmic Functions

This calculus video tutorial explains how to find the indefinite integral of logarithmic functions.  This video provides a simple formula that can help you to achieve it as well as explain how to show your work.

Center of Mass and Centroid Problems

This calculus video tutorial provides a basic introduction into the center of mass of a system also known as the centroid.  It explains how to find the x and y coordinates of the centroid of a planar lamina which is a 2d region.  The center of mass occurs where an object or a region can be balanced by a pencil if gravity is the only force acting on it.  This video contains plenty...

Hydrostatic Force Problems

This calculus 2 video tutorial explains how to find the hydrostatic force on a plane surface submerged in water.  This video contains plenty of examples and practice problems of finding the fluid force acting on a vertical submerged plate.  Examples include the square, right triangle, isosceles trapezoid, and the semicircle.  The weight density of water is 9800 N/m^3 or 62.4 lbs/...

Homogeneous Differential Equations

This calculus video tutorial provides a basic introduction into solving first order homogeneous differential equations by putting it in the form M(x,y)dx + N(x,y)dy = 0.  You can solve it by substitution using the equation y = vx and dy = xdv + vdx.  Following the change of variables, you can integrate the differential equation by separation of variables.  This video contains ple...

First Order Linear Differential Equations

This calculus video tutorial explains provides a basic introduction into how to solve first order linear differential equations.  First, you need to write the equation in standard form [y' + P(x)y = Q(x)] and then identify the functions P(x) and Q(x).  Next, you need to determine the integrating factor I(x) using the formula I(x) = e^(integral of P(x)dx).  Finally, you can use an...

Bernoulli's Equation For Differential Equations

This calculus video tutorial provides a basic introduction into solving bernoulli's equation as it relates to differential equations.  You need to write the differential equation into the standard form of Bernoulli's equation and identify P(x), Q(x), and n.  If n = 0, you have a linear differential equation.  If n = 1, then you have a differential equation that can be solved by s...

Slope Fields - Calculus

This calculus video tutorial provides a basic introduction into slope fields.  It explains how to draw a slope field using an x-y data table given the differential equation.  It also explains how to sketch the solution curves or the general solution of the differential equation on the slope field and how to verify the solution of the differential equation by integrating using separati...

Converging and Diverging Sequences Using Limits

This calculus video tutorial provides a basic introduction into converging and diverging sequences using limits.  It explains how to write out the first four terms of a sequence and how to determine if a sequence converges or diverges by finding the limit of a sequence.  If the limit exists and it equals to some constant L as n approaches infinity, then the sequence converges.  I...

Monotonic Sequences and Bounded Sequences

This calculus 2 video tutorial provides a basic introduction into monotonic sequences and bounded sequences.  A monotonic sequence is a sequence that is always increasing or decreasing.   You can prove that a sequence is always increasing by showing that the next term is greater than the previous term.

Convergence and Divergence - Introduction to Series

This calculus 2 video tutorial provides a basic introduction into series.  It explains how to determine the convergence and divergence of a series.  It explains the difference between a sequence and a series.  This video includes examples and practice problems with geometric series, harmonic series, and the telescoping series.  It also discusses the divergence test.

Calculus 2 - Integral Test For Convergence and Divergence of Series

This calculus 2 video tutorial provides a basic introduction into the integral test for convergence and divergence of a series with improper integrals.  To perform the integral test, let the sequence be equal to a function that is continuous, positive, and decreasing on the interval [1, infinity).  If these conditions are met, then the infinite series will converge if the definite int...

Calculus 2 - Geometric Series, P-Series, Ratio Test, Root Test

This calculus 2 video provides a basic review into the convergence and divergence of a series.  It contains plenty of examples and practice problems.

Power Series - Finding The Radius & Interval of Convergence

This calculus video tutorial provides a basic introduction into power series.  it explains how to find the radius of convergence and the interval of convergence of a power series using the ratio test.  If the limit of the ratio test is zero, the power series converges for all x values.  If the limit is infinity, the power series converges only when x equals c such that the power ...

Power Series - Differentiation and Integration

This calculus 2 video tutorial provides a basic introduction into the differentiation and integration of power series.  It explains how to find the derivative and the integral of a function represented as a power series.  In addition, it explains how to find the radius of convergence and the interval of convergence using the ratio test after differentiating a power series and integrat...

Power Series - Representation of Functions

This calculus 2 video tutorial provides a basic introduction into the representation of functions as power series.  It explains how to represent a function as a power series centered at 0 and centered at some value c.  It also explains how to approximate function values using geometric power series.  This video also explains how to find the radius of convergence and the interval ...

Taylor and Maclaurin Series - PDF Worksheet

Taylor and Maclaurin Series

This calculus 2 video tutorial explains how to find the Taylor series and the Maclaurin series of a function using a simple formula.  It explains how to derive power series of composite functions using known Maclaurin series of elementary functions.  This tutorial has a ton of examples and practice problems.

Binomial Series

This calculus 2 video tutorial provides a basic introduction into the binomial series.  It explains how to use the binomial series to represent a function as power series in sigma notation or summation notation.  This video contains plenty of examples and practice problems.

Finding Area In Polar Coordinates

This Calculus 2 video tutorial explains how to find the area of a polar curve in polar coordinates.  It provides resources on how to graph a polar equation and how to find the area of the shaded region.  It contains plenty of examples and practice problems on how to find the area of one loop or of one petal and how to find the area of the inner loop as well.

Calculus 2 Final Exam Review

Calculus 2 Final Exam Review - Part 2

This calculus 2 final exam review covers topics such as finding the indefinite integral using integration techniques such as integration by parts and trig substitution.  It discusses how to find the arc length of a function and how to graph parametric curves.