γ(t)=t^2e^it, 0 ≤t ≤3π. Find the value of γ(π/2).

Q: хах 3. S cos (2-3x2)

A: To evaluate the integral ∫x dxcos2-3x2.

Q: Fin 7-√42 X mZX = Y O 21/14 N

A:

Q: (f) / sec“ y dy. tan5

A:

Q: What is the equation of the function? O A. y = ()* ов. y = 3 OC. y = 2(- 3. O D. y = 2(3) 2/3

A: General equation of exponential function :

Q: Find Sta | tan (ay) dy 32.

A: We have to find integral of given function.

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

A: We have to find the indefinite integral

Q: 3 + 2/5x-3 dx. Find 4x+1 - Vez

A:

Q: Differentiate.

A: We use the quotient rule

Q: Which of the following functions is a solution of the exact equation? (6x + 4y)dx + 4xdy= 0.

A:

Q: Find the domain and the range y= V1- sinx

A: Given function: y=1-sinx

Q: V101 ft 12 ft

A:

Q: y= c¡x+c2x²

A:

Q: 2, then the conju

A:

Q: needed. That way you'll have better chance x2 + + 2x +3 dx x3 +3x2 + 9x a. #13. 26+

A: Since you have asked multiple questions in single request,  So we will be answering only first…

Q: _3. lim (17x – 4) х--18 А. -140 В. 310 С. -310 D. DNE

A:

Q: Find dey if 2:t - t' ond y:t-t". dx

A:

Q: Q3/ Determine whether the following functions are harmonic or not. 1. 3xy + 5xy - 2y 2. 3x²y + 2x -…

A:

Q: 8. (2x° – 3x) dx

A:

Q: 3. tan x dx

A: Formula: tan2x=sec2x-1

Q: d2y at the point (2,) 48. Given yax-i.find -1, find - at the point|2, ах x

A: Given:The function y2x2 = 1.The point (2,1/2).

Q: If fxl = -:2(1- x), find o pla farmula (x). 1-メ

A: Given function is f(x)=2(1+x)=2(1-x)-1 Using binomial formula for 1(1-x) we have,…

Q: 3D5 in.

A: The area of the circle can be computed using the formula: Area=π r2 Where, 'π' is the constant value…

Q: Solve : 7tan³x – 21 tan x = 0 T 2n 4n 57 A.,I, C. 3' 3 3' 3 3 В.", п, D. 0,,,, 3' 3 3

A:

Q: ·S. 144. dx x6 = x² -

A:

Q: Evaluate Set 7x cos (6x) dx. Sex cos (6x) dx =

A:

Q: Circle One. Is x=-4 a solution to the function: f(x) = x'+6x +1 lx+6 YES or NO

A:

Q: 12. fe"dk = А. 1-е! В. -1-е! C. e+e D. -1+e 13. felnx dx = A +k В. +k C. e +k D. 2ehr +k Inx 513

A:

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.