Academic Videos (Solved Examples)

Weierstrass Substitution: Integral of 1/(cos(x) + (3/4)sin(x)) dx

Integration by Partial Fractions: Integral of 1/((x - 1)^2*(x – 2)^2) dx

Integration by Partial Fractions: Integral of (4x^2 - 21x)/((x - 3)^2*(2x + 3)) dx

Integration by Partial Fractions: Integral of 3/((x + 1)(x^2 + x)) dx

Integration by Partial Fractions: Integral of (x^2 + 3x - 44)/((x + 3)(x + 5)(3x - 2)) dx

Integration by Partial Fractions: Integral of 1/((x - 2)(x - 3)(x + 2)) dx

Integration by Partial Fractions: Integral of (x^2 + 11x)/((x - 1)(x + 1)^2)) dx

Integration by Partial Fractions: Integral of (2x - 1)/(x^2 - 5x + 6) dx

Differential Equation Variation of Parameters: x^2*y'' + xy' = cos(ln x)

First Order Linear Differential Equation: x^4*dy/dx + 2x^3*y = 1

Integration by Partial Fractions: Integral of 1/(x(2x + 1)) dx

Integration by Partial Fractions: Integral of 1/((x - 2)(x - 4)) dx

System of Linear Equations : 4 variables, 3 equations

Average value of y = x^2 - 3x + 6 on the interval [0,9]

Derivative using Limit Definition: y = 1/sqrt(x - 1)

Integration by Parts: Integral of sin x cos x dx

Find 2nd solution: (1 - 2x - x^2)y +2(1+x)y -2y = 0 , y1 = x+1

Homogeneous Differential Equation: dy/dx = (x^2 + y^2)/xy

Homogeneous Differential Equation: dy/dx = (x-y)/x

Inverse Laplace Transform of function including natural log: ln(1 + 1/s^2)

Differential Equation Method of Frobenius: 2xy + 5y + xy = 0

Differential Equation Method of Frobenius: 2xy - y + 2y = 0

Differential Equation Undetermined Coefficients: y - 4y = e^x cos x

Linearly independent or linearly dependent: f1(x) = x , f2(x) = x - 1 , f3(x) = x - 2

Double Integration: Integral of xy*sqrt(x^2 + y^2) dy dx, y = 0 to 1 , x = 0 to 1

Integration by parts: Integral of x sin 2x dx

Integral of sec^2(x)csc^2(x) dx

Integral of (5x^3 + 7x -1)^(3/2) (15x^2 + 7) dx

Find the volume of the solid that lies under the plane 4x + 6y - 2z + 15 = 0

Integration by Parts: Integral of cos(x)tan^-1(sin x) dx

Integral of sin(x)sqrt(1 - cos(2x)) dx

Integral of (sin^8(x) - cos^8(x))/(1 - 2sin^2(x)cos^2(x)) dx

Charge density at (x,y) is σ(x,y) = 2x + 4y. Find the total charge on the rectangle.

Change integral to polar coordinates: e^(-x^2 - y^2) dA where R is region bounded by semicircle

Integration by trigonometric substitution: Integral of x^4/sqrt(1 - x^2) dx

Find the volume of the solid lying under the elliptic paraboloid x^2/4 + y^2/9 + z = 1

Determine the absolute extrema of the function f(x) = 2x^3 -3x^2 - 12x + 1 on the interval [-2,3]

Integration by u Substitution: Integral of cos^2(x)*tan^3(x) dx

Limit of (sqrt(x) - 3)/(x - 9) as x approaches 9

Find the volume of the solid enclosed by the paraboloid z = 2 + x^2 + (y - 2)^2

Laplace Transform of unit step function

What is the difference between timesharing and multiprogramming systems?

Limit of (x - 1)/(sqrt(x + 3) - 2) as x approaches 1

General Solution of the augmented matrix: [1 3 4 7 ; 3 9 7 6]