For atims (3) to (8) refer to the À = x2i + (2x"-y)j - yzk and = 3x²y + y² z? followning = X? %3D (3) ♡ Ø (4) D.A

Q: dy 9. Find for y=xVx+ 1

A:

Q: 2. If y = xlnx,

A:

Q: |(9x - 5) dx, given the following. Calculate 2 X-dx 3 19 dx = 3 %3D xdx =

A: Property of Definite integration: If the upper and lower limits are the same then the integral is…

Q: y - 1 %3DCOS (7x*) dy dx %3D

A:

Q: 1. у%3D х3 — 2x2 + 3х — 5 y = 3 — 2х2 + 3х — 5 dy — Зx2 — 4х + 3 dx

A: Given: y=x3-2x2+3x-5

Q: MA 1. Find the following, a. f(5x2 – 6x +3)dx = OWI +2 4t %3D dt

A:

Q: s.fx 5. x3 sin 3x dx

A: We have to find the indefinite integral

Q: ve

A:

Q: (3x² -8)dx= а. 3 b. 1 С. 9 d. 5

A:

Q: 1 dx %3D x-3V2x-4+2

A:

Q: .3 9. dx dy y2

A: Find the double integration.

Q: (1-y)dx – xydy= dy

A: 1-y2dx-xy=dy1-y2dx=dy1+xydydx=1+xy1-y2…

Q: r4 3 +1 d y? 1

A: We will solve the problem

Q: II. Evaluate the following. 1. 2x+4x-3 dk 2. Sx-8 x-2 3. J vx*-2x'+x*dx

A:

Q: find dy. y =2√x/3(1 + √x)

A: we have to find the derivative y=2x3(1+x)

Q: proke that lose ch?e %3D (0nsiden

A: To prove that Cosech^2x=coth^2x-1

Q: 1 The value of f|5x – 3|dx is

A: Integration of the absolute valued function

Q: dy %3D xp

A:

Q: dx 1+ 3/2 х

A: We need to integrate the given integral.

Q: 1- S dx -4 4

A:

Q: dx 4. 1- 2cosx

A: The integration of the 1/(1-2cosx).

Q: | xVx-2 dx

A:

Q: 1 10. dx x² Vx² – 4 -

A:

Q: ³+1 2x²5x 3 S dz.

A:

Q: 00 1 dx 2х + 1)4.

A:

Q: 1 -dx. J x2 + 2x +2

A:

Q: re? e3 1 dx dy dz xyz

A:

Q: 1. [²+3x - 4)dx

A:

Q: (5a.4) dn 1 (2,2) (a?-x +1

A:

Q: d 4. Simplify. dx (t² + 1) dt 2x

A:

Q: Sketch x = 1/y.

A: Sketch.x=1y

Q: #8

A: We are going to use the formulas:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.