Approximate - -1x+3 -dx using trapezoidal rule with n=4 and Simpson's rule with n=4.

Q: Differenticte y= (SN( 3))/ (4t 5cos (2x))

A: Given :y=sin(3x)4+5cos(2x)

Q: (x – y)(4x + y)dx + x(5x – y)dy = 0.

A:

Q: 2 3x + 8x + 4 A) x+ 5

A: To determine:

Q: (D'+3D+2)y=e

A: See the attachment

Q: a

A: Here we have to evaluate I=∫xex1+exdx ...........................(1)

Q: By using chain rule Find dy/dx iff- u=-1, x=-1

A:

Q: b) if J(zf64)} - 39ga) ) ce = Sin () %3D and S(3f (x)+9 6)) dx = tan () 2. 2. +596)) dx

A:

Q: 6) 1) (2x²-3x+2)dx -5

A: Given that integral is

Q: Estimate I = = I~|| +21 (8z + 82²)da using midpoints and n = 3 subintervals.

A:

Q: Lion 1-y If x = Show that 1+y dy V1-y

A:

Q: e?y - dy (ve)" – 1

A:

Q: Q3) Find dy/dx if 1- y= In /x 2- y3xsin

A: 1) d(ln(x))dxApply the chain rule: 12ln(x)d(ln(x))dx

Q: tdt (1+t*)(arctan² t² + 4 arctan t² + 5)

A: Use the substitution method to solve the integration.

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.