dy for the following fi dx Exercises (20.8): Find 1) y = en(x)–In(1+x) 2) y = In %3D

Q: d x° In x C. dx d [x3 d In x+ 3 [In x] -. 3 dx 3 dx

A: Given:

Q: B1. Verify fy = fx for the function f(x,y) = ln(2x- 3y). %3D xy

A:

Q: Evaluate J dx √x(1+√x)

A: ∫1udu = lnu +C

Q: 6. 3(у + 1) dx %3D 2х dy

A:

Q: dy If y = x (e* - 1), then %3D 6. dx

A: Given: y=x^2 ((e^ x)-1) To determine: d y/dx

Q: Find if y = (x² – 1) (x³ + 2). dx

A: We expand the given expression and then use power rule to find the derivative.

Q: 1-√x)³ 3 √x dx

A:

Q: Find y in terms of x given that (1+ x) = x²y and that y = 2 when x = 1. dx

A: The given differential equation can be simplified as shown below: (1+x)dydx=x2y     ⇒…

Q: Evaluate x(x2 + 1)3 dx.

A: Given ∫x(x2+1)3dx

Q: 2/3 Find y" 11 y = (x* + x) %3D

A:

Q: te the following: 2x dx x - 4 dx

A:

Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differential equations. The most important aspect of this theory is error analysis.