#mesdualityUnmoderated tagAll postsTrendingHotNewPromotedPayoutsmes in #calculus • 3 years agoIntegration using Computer Algebra Systems (CAS)In this video I go over the use of computer algebra systems (CAS) and how they are used to calculate integrals very quickly. From my earlier videos on using Tables of Integrals I…mes in #mathematics • 3 years agoCorollary of Continuity Theorem: ProofIn this video I go over a simple corollary theorem which is a direct result of the continuity theorem which I went over in my earlier video (video link below). This theorem…mes in #mathematics • 3 years agoPartial Fraction Decomposition: Non-Linear FactorsIn this video I go over further into partial fraction decomposition and show how to decompose rational functions that have non-linear factors (or irreducible factors) in the…mes in #mathematics • 3 years agoPartial Fraction Decomposition: General TechniquesIn this video I over an introduction on partial fraction decomposition and go over some general techniques in decomposing a rational function that has unique linear factors in…mes in #mathematics • 3 years agoIntegration by Partial Fractions: Example 5In this video I go over another example on integration of rational functions by partial fractions and this time integrate a function that has a non-reducible non-linear factor in…mes in #mathematics • 3 years agoIntegration by Partial Fractions: Example 6In this video I go over another example on integration of rational functions by partial fractions and this time go over an example that involves a non-linear function in the…mes in #mathematics • 3 years agoTrigonometric Substitution for Integrals: Example 6In this video I go over another example on trig substitution for integrals and this time show that sometimes we need to further simplify the integrand to enable trig substitution…mes in #mathematics • 3 years agoIntegration by Partial Fractions: Example 3In this video I go over another example on integrating rational functions by the method of partial fractions and this time solve the integral of 1/(x2 - a2) where a is not equal…mes in #mathematics • 3 years agoTrigonometric Identity: Integral of 1/(x^2+a^2)In this video I go over a useful trig identity which is basically that the integral of 1/(x2+a2) = 1/a*arctan(x/a). This identity is derived from the derivative of arctan(x) or…mes in #mathematics • 3 years agoIntegration by Partial Fractions: Example 2In this video I go over another example on integrating rational functions through the method of partial fractions and this time integrate the function (x2+2x-1)/(2x3+3x2-2x).…mes in #mathematics • 3 years agoIntegration by Partial Fractions: Example 1In this video I go over an example on using the method of partial fractions for integrating rational functions. In this example I go over the integral of (x3+x)/(x-1) and break…mes in #mathematics • 3 years agoPartial Fraction Decomposition: Summary and Higher PowersIn this video I summarize the basic linear and quadratic factors cases for partial fraction decomposition as well as talk briefly about factors with higher powers. It is also…mes in #mathematics • 3 years agoPartial Fraction Decomposition: Proof of General Case with Linear FactorsIn this video I go over an extensive proof of decomposing rational functions for the general case with linear factors. Although the video is very long and detailed, it follows…mes in #mathematics • 3 years agoTrigonometric Substitution for Integrals: Example 7In this video I go over yet another example on trig substitution for integrals and this time solve the integral of the function x/sqrt(3-2x-x2). In this example we first have to…mes in #mathematics • 3 years agoIntegration by Partial Fractions: Example 4In this video I go over another example on integrating rational functions by the method of partial fractions and this time go over an example that requires both polynomial long…mes in #mathematics • 3 years agoIntegration by Partial FractionsIn this video I go over an introduction on the method of partial fractions for integrating rational functions. Basically rational functions can be simplified by breaking them…mes in #mathematics • 3 years agoThe Area of an Ellipse (and Circle)In this video I go over further into trigonometric substitution and this time do example 2 of the example series which so happens to be determining the area of an ellipse using…mes in #mathematics • 3 years agoTrigonometric Substitution for Integrals: Example 5 Part 2: Hyperbolic Trig SubstitutionIn this video I go over the same example 5 on trig substitution for integrals which I did in my last video but this time solve it using hyperbolic trig substitution instead.…mes in #mathematics • 3 years agoTrigonometric Substitution for Integrals: Example 1In this video I go over an example on trig substitution for integrals and solve for the integral of the function sqrt(9-x2)/x2. In this example I write the variable x in terms of…mes in #mathematics • 3 years agoInverted EllipsesIn this video I go over inverted ellipses which are basically vertical ellipses or have the foci on the y axis. The inverse of the ellipse is found by simply switching the x and…