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

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A:

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A:

Q: Integrate the following expressions: Sex-e (2x – e*). dx !! (x + cos2x). dx "/2 X cos2x.dx

A:

Q: 3. Find y': y = 5sin3x

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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: Evaluate Cn xp*q" Xn-x for the values of n, x, and p given below. 1 n = 4, x = 1, p= X_n-x Cn,xp*q°…

A: Solution:

Q: Find if x = and y = t +3 (t+1) 1 %3D dz O a. none of these O b. (t+1)°(4t + 3) Oc름(t-1)°(4t-1) O d.…

A:

Q: (1 + VA)³ -dx. (c) Evaluate /

A: To evaluate the given integral.

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

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

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: Q.2 Evaluate : P;(x)dx=

A:

Q: For numbers 18-20 18. Given the function f(x) = cos(5x), 0<x<2n

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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: 1.557 B) In (x) dx + | (2 – x) dx 1.557

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Q: At which octant will you find (-8, 13, -1/2)?

A:

Q: Find dy/dt. y cos (rtt-10) %3D Select one: A. -5T COs (Tt - 10) sin(7tt - 10) B.-5Tt sin (rtt - 10)…

A:

Q: Evaluate √ x²ekx dx. (Helpful hint: √ ekx dx = €** + C) ekx k

A: To evaluate the following integral.

Q: B. Evaluate the following .5 |x² – x - 6| dx -5 1.

A: The question is determine the question is evaluate the definite integral. Note -  As per our…

Q: Solve the following ODE * (y+x*y²) dx+x dy = 0

A:

Q: x² – 1 - Evaluate f dx x4 +1

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

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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.