4. Find the value of the integral 223 + 5 'zp- c (z – 1)(2² + 9)* taken counterclockwise around the circle (a) |z – 2| = 2; (b) |2| = 4.

Q: (2rz - yz)dr + (2yz – zr)dy – (² – xy + y²)dz = 0.

A: Given that, 2xz-yzdx+2yz-zxdy-x2-xy+y2dz=0

Q: Prove : (x2 + 2x + 2 )dx > 0

A: The given integral is ∫-10x2+2x+2-x2dx The integral has been rewritten∫-10x2+2x+12x2dx Apply…

Q: 1 dx = x(x* + 1) Select one:

A:

Q: Finds 2) S 12x-31 dx

A:

Q: P4: x3 (x² + 1)3

A: Use the algebraic substitution and solve the integration.

Q: Find r'(t), r"(t), r'(t) · r"(t), and r'(t) × r"(t). P(C) = 21²1 - 48 + ²P²H 2³k r(t) 3 (a) r(t) 3it…

A:

Q: 4x2+6x+1 dx (x+3)(x²+2x+2)

A: =?

Q: 4. (D2 – 5D + 6)y = 15sinx – 15cosx -

A:

Q: 3 7) Evaluate: f(-x² + 4x − 1)dx 1

A: Given, ∫13(-x2+4x-1)dx

Q: d) S 2xe* dx

A:

Q: Suppose that I'm (f`∞x) = (x (24-1) and f(0) = 3-2i, f(1) = 6 -21, Find f(1+i)

A: Given that Imf'z=6x2y-1 To find: f(1+i).

Q: [₂ x³ √√x² +1 3

A:

Q: 1 Evaluate : dx. (1+x)Vx -x X-X

A:

Q: [° [² (5 x² + y²) dx dy

A:

Q: = (b) ſ sin (7(x – 2y)²) dA, where T is the triangle bounded by x – 2y T 1, y = −3x and 5y = -x.

A:

Q: dx 4x2 + 9

A: Use substitution.

Q: Find all residues of the function z (2-2) not including the residue at infinity. "

A:

Q: Find the integral 52? + 3х — 2 dx +C x3 + 2x?

A:

Q: Evaluate: 2 (1) (2-3)* dx 1 1 dx x + 5 (2)

A:

Q: y"' – 3y" + 4y = 6+80cos(2x)

A:

Q: dr. +37-10z

A: We have to evaluate the given integral.

Q: (x+6) 15. J (x+2)2 dx

A: Here I am attaching image so that you understand each and every step.

Q: 11. Evaluate 9-y² LS [[V²=2³² (x² + y²) ² dx dy -3 0

A: We need to evaluate the double integral given by :

Q: dx Use a trig substitution to evaluate x³ Vx² x > 1. 1 6. -

A: