Laplace inverse (ln(3x))

Q: Use Simpson's Rule to evaluate the following. n = 10 +3 1 dx J-3 1+x²

A: SOLUTION-

Q: √ 2*+3* dx 5*

A:

Q: Calculate E(X)

A:

Q: inverse of sec x?

A:

Q: Se-*cos(5x) dx

A: Given : ∫ e−xcos(5x)dx

Q: QUESTION 2 Consider the following information about 3 random variables, X, Y and Z. X|Y-Gamma(2 Y2,…

A: Given: X/Y ~ Gamma(2Y2, Y) Y~ N(2, 5)   E(X/Y)=2Y2Y=2Y

Q: Hicit Differentiation yt= 4xy

A:

Q: dy Evaluate dx at point (4,2) given 3(x² + y²)² = 100(x² – y²).

A: Answer and explanation is given below

Q: Please calculate H(x) -Mx dx H(x) = [°e¬M* dx

A:

Q: Cose 2 03D and

A:

Q: du / (1 - e")2

A:

Q: Prove the identity arcsinhx=ln(x+√1+x2).

A:

Q: Suppose that X is a random variable with distribution function given by I< 1, 1<r< 2, 2 <x < 3, 3<r.…

A:

Q: e cos (2x) dx

A: The given integral ∫e-xcos2xdx can be evaluated as, Let,  I=∫e-xcos2xdx By applying integration by…

Q: Explain how to find a differential of a function.

A: Let us consider a function f(x) and its differential to be f'(x)

Q: The expression of Absorption's law is given by what?

A: The expression of Absorption's law is

Q: Evaluate ax xm-1 sin bx dx in terms of Gamma function. -ax

A: We use the special results of Gamma function to solve this problem as in next step.

Q: Jse logarithmic differentiation. sin(w²) + log w b = (csc (Tw))10/tan-1(w³)

A: