Integration, derivative, and limits

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• U substitution

  U substitution is explained using the example S4x(x^2+1)^5dx without and with limits of integration.

• Question about please explain the process of U substitution

  You can put the limits of integration in terms of by using the equation , or you can ignore the limits of integration while working with , and instead of adding plug in the original given limits of integration after you have switched back from

• Derivative of the Function and Definite Integral

  Find the indefinite integral: This integral can be found using integration by parts. We will choose and . Taking the derivative of u and the integral of dv gives and .

• A problem with Legendre Equation & the Legendre Polynomials

  Part (b) The thing that made this work was this derivative : d/dx(f'g-g'f)=f''g-g''f and of course their hint! Regards, Jan The problem is solved by integration and evaluation between the limits and algebraic manipulation

• Integration and Fundamental Theorem Calculus

  The expert examines integration and fundamental theorem calculus.

• Time dependent Schrodinger equation (TDSE) in operator form

  We know that: Then: Since this is a spatial integral (integration over space only) we can apply the time-derivative directly on the inegrand (all limits are from -∞ to ∞): Since the Hamiltonian is Hermitian: The expert examines Time Dependent

• Integral, Continuity and Limits

  The Leibniz derivative and the Poisson integral are applied. The solution is detailed and well presented.

• Indefinite Integral

  x): Integral { f(x) } dx = F(x) + C Then the value of the definite integral is given by: F(b) - F(a) That is, we find the anti-derivative and substitute the lower and upper limits in place of x and find the difference.

• Differentiate, Find the area of the section of the hyperbola

  x^2 / a^2 - y^2 / b^2 = 1 can be written as y = (b/a) √(x^2 - a^2) ∫ y dx = ∫ (b/a) √(x^2 - a^2) dx = (b/a) * (1/2)[x√(x^2 - a^2) - (a^2) ln{(2 √(x^2 - a^2) + 2x}] = (b/2a) [x√(x^2 - a^2) - (a^2) ln{(2 √(x^2 - a^2) + 2x}] Applying the limits of integration

• derivative of the function

  Compute the derivative of the given function and find the equation of the line that is tangent to its graph for the specified value x = c. (Compute the derivative of the function from the definition only, using limits.