r1+ni Q1. Evaluate *e²dz along the path shown in figure below. (25 Marks) n/2 Q2. Evaluate . dz where C is: (25 Marks) (z2+1) cosnz 3/2 1. Iz - 2i| = 0.5 2. %3D

Q: Use one of the formulas in the equation A = fexdy = fc-y dx = 1/2 fex dy - y dx to calculate the…

A:

Q: dy Q10., Solve (1+ x²) + y = tan¬1x. dx

A:

Q: 8. Evaluate: ſ V1– cosx dx A. V2 cosx + C c-2 sin를 + C B.-VZCOS를 +C D. -VZcos + C

A:

Q: dæ . (x – 3)væ² – 6x + 5 Evaluate 2.

A: To evaluate the following integral

Q: The tanh$ (2x) sech (2x) dx is equal to O A. None of the choices in the list. O B. tanh (2x) +C OC.…

A: Given integral is  ∫tanh52xsech2xdx

Q: L(cos3t) = S .a O s²+9 S .b O s+9 s2 –9 3 s2+9

A:

Q: 19. Use u substitution to evaluate. x5 So (4+x6)³) dx

A: Evaluation of the definite Integral by substitution method

Q: O Solve the eguation, Kdz x dz - gdz +ze (tya) Ans OF THS + -z) =0

A: This is linear equation so we can use Lagrange auxiliary equation to solve this problem.

Q: Q3. Evaluate ". -2n sin²0 de 5+4cos0

A: To Determine :-  ∫02π sin2 θ5 + 4 cos θ dθ

Q: 7x + 6 Find dy for y = dy =

A:

Q: Evaluate J e*sinh2x dx Select one: O a. ex 3X а. e- + C 6 2 O b. e-X e 3x + C 6. O c. none of the…

A: The given integral is ∫e-xsinh2x dx

Q: Evaluate ¹/2 1 3 — 1 dx.

A:

Q: | V49 + x² dx (7) (8) / - ² x – 4 dx x In x

A: Solve by integra

Q: d² y If ax? dx? 3. Find + 2 hxy + by = 1, h? - ab Ans. (hx + by)

A: So in this we have to differentiate twice. I'm providing hand written solution.

Q: 3x + 2 dx. (x² +9)(x– 4)x Find the principal value of - 00

A: The given problem is related to complex analysis. First we consider the integrand function as f(z)…

Q: d. Evaluate dr ((5x² + 10)e) at r = 2.

A: We will differentiate the given expression using the product rule and then put X equal to 2

Q: Find the la x b|, if a = 3i + j + 2k and b = 2i – 2j + 4k %3D 13.86 42.49 32.91 24.04

A:

Q: Find dy for x5 + 2y* = 5y dx

A: Derivatives can be defined as rate of change of function with respect to an independent variable.…

Q: 9 = dy

A:

Q: Evaluate the following. 21. (2x +1)(2x* + 3x -- 4) dx (22.)(x +6x –1) (x+3) dx 2.3. (2x-1)(5x- 5x+4)…

A: We have to find the integrals: 21.  ∫2x2+12x3+3x-42 dx22.  ∫x2+6x-14x+3 dx23.  ∫2x-15x2-5x+43 dx…

Q: Find the area S of the shaded region in the figure if ƒ (0) = 0² + 30. Note that 0 varies from 0 to…

A: To find the are S of the shaded region in the figure if fθ=θ2+3θ Note that θ varies from 0 to…

Q: 3. Which of these products is negative? Select all that apply. A. 6. (-3) B. -2.(-4)

A: NOTE: Refresh your page if you can't see any equations. . the first option is…

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: A. Evaluate Inx dx. 2x B. Evaluate [(7x-10)dy dx. 0 x?

A: Note: Since you have posted multiple questions. We will solve the first question for you. If you…

Q: | (cscx + 3 e3* š + 6" – 7) d.æ -

A: Given: ∫(csc2x+3e3x+6x-7)dx

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.