Let R be the rectangle with vertices -1-i, 8i, 8+i, -1+i. Use residues to evaluate the following integral. 1 L (²1 + 2 2² 3 R 3i dz

Q: | 4z(z* + 1)* dz Calculate: 0.

A:

Q: find x, y € Z such that 2261x + 1275y = gcd(2261,1275).

A: we want to find the greatest common factor  we will use Euclid's algorithm 2261=1275×1+986 -----1)…

Q: 1. [Easy] Consider the 2 x 2 square [-1, 1] × [-1,1]. Evaluate: 2x2 square Why should the answer be…

A:

Q: 13 14 15 17 0 6 (x + 7)²dx = 618 1107 10

A: Given query is to find statement is correct or not.

Q: So 3 Vit7x dx U-substiutson.

A: Use u substitutions to integration

Q: x y ● = Find the dot product of 1 18 0 — -2 and y = 1 2 4 ●

A:

Q: Calculate the triple product ā · (b x c), where ā =,b=, and č=.

A: Given vectors  a→=2 , -4 , 1b→=0 , 3 , -1c→=5 , -3 , 3

Q: 6х —9 4.) dx 22— 3х +2

A:

Q: 5л — 2 dx x2 +1 10.)

A:

Q: Evaluate dxdy √√3x + 4y over the rectangle [0,3] × [0,4].

A: We find required integral by using Fubinis method.

Q: x.y = Find the dot product of X 0 []. 0 3 [] -2 -3 and y=-2

A: The given vectors, and .The aim is to find the dot product .

Q: a = 2i + 3j - k, b = -4i + 5k |

A: Given: a=2i+3j-kb=-4i+5k

Q: Find the distance d between z1 = (8+ 8i) and z2 = (-8+ 8i).

A: