The following table shows the annual number of PhD graduates in a country in various fields. 1990 1995 2000 2005 2010 Natural Sciences 70 130 330 490 590 Engineering 10 40 130 370 550 Social Sciences 60 110 270 470 830 Education 30 40 130 210 520

Q: s(VE + E dx

A: We want to integrate the given function.

Q: 4xy, Amdl ly 2.

A:

Q: (a)

A: Given,           jj

Q: In(52) dx 3

A: To evaluate

Q: Soluce for dy dx Tn x +Vx y=.

A: we can find the differential using division rules as below

Q: S, (x3 + e*) dx

A:

Q: 5+(54 33)

A:

Q: ☺ cosh"z= Loy {2+/2

A:

Q: iate ſ In(x + v1 +x²)dx

A:

Q: Q6/(A)Evalute ex² dxdy.

A: Given: ∫02∫y21ex2dxdy Evaluate the given integral. If the order of integration is x, y then…

Q: dx 7). JaVx-1

A:

Q: 4 dx 8)

A: Consider the given definite integral.

Q: S sec ydy

A:

Q: [x³J2]=X³J2 dx صواب ihi

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: 9. 7 5+ -dx

A:

Q: (3 In z + 2)4 dz Z

A: The given integral is (3 lnz +2)4/z.

Q: Evaluale the to 312 bwiny dx 12

A:

Q: 8. dx (36-262

A: Integrate by using trigonometric substitution

Q: dx (2х — 5)10 Integrate -

A: We have to solve the given integral : ∫x(2x-5)10 dx = ?

Q: dx. V9-2

A: Solution is given below

Q: ー dx

A:

Q: e-(6x+5y) dxdy

A:

Q: Evaluate e dt 0.2

A: We have to use standard gamma integration here.

Q: 3X (02-60,9)y=e" (x+2) %3D

A: Given differential equation is  (D^2 - 6D + 9)y = e^3x(x+2)

Q: dx 10. J V2x2-1

A: See the details solution in below

Q: dx Vx2 - 1

A:

Q: 24 dx (144x²+1) Evaluate S- 2

A: Here we have to find the integral.

Q: cln3 dx (b) (10 points) Ф) (10 роints) z et n2 e*-e

A: We use the definition of the integral of functions and partial fractions to evaluate the given…

Q: LX Solve the dlifferontial equation using the power series methbd.

A:

Q: 1 S² = y e2y dy

A:

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

A:

Q: Reversing the order of integration: (2) O dy.dx- dx dy ........ O 2

A: Reversing the order of Integration : Consider a double integral over a domain D, the we can express…

Q: Re(2²) = 1

A: To solve the equation: Re(z2)=1                                                      (1) Here z is a…

Q: Y (t)

A:

Q: P(A)= 0.33, P(B)= 0.44, P(A and B)= 0.16 Calculate P(A and B')?

A: Answer: From the given data, P(A) = 0.33 P(B) = 0.44 P(A and B) = 0.16

Q: уху + ху %3D 7, у"

A: x.y+x.y=7we know thatddx(uv)=vdudx-udvdxv2    and ddx(u.v)=udvdx+vdudxdifferentiate…