Calculate the line integral of the vector field F = (5xy, x, y + z) around the boundary curve, the curl of the vector field, and the surface integral of the curl of the vector field. The surface S is given by z = 1x² - y² for x² + y² ≤ 1 oriented with an upward-pointing normal. (Use symbolic notation and fractions where needed.) [₁ F. dr = curl(F) = Ic curl(F). ds =

Q: 3.3 31 3 O 3 O 3평 37

A:

Q: dx 0 4-x

A: To evaluate the integration.

Q: 2. 6. 1.

A:

Q: 25. 1 | 1 1 + 1 - 1

A: Solution is done in step 2

Q: 10.0

A:

Q: 1 1 dx 3 5 x +x4

A:

Q: Find .6 7 LT." 3 4 xy dydx.

A: Given that the integral ∫36∫47xy dydx. Find the value of given integral.

Q: 8. arctan (-1)

A:

Q: Alt 8. 5. 14.

A:

Q: d) | 4f(x)| dæ =

A:

Q: 1.6+0.4(x+6)+3.2

A: To simplify the expression means writing it in the simplest form.

Q: 4. w/- 4. 2.

A: Given:

Q: 4 yd

A:

Q: 10 8. ID 116

A: Introduction: The division is one of the four basic mathematical operations, alongside addition,…

Q: 3,

A: Use 2 chords power theorem

Q: 20 9.

A:

Q: 29 14

A: It's trigonometric question so I'm providing hand written solution for better understanding.

Q: 8. 2 k=1 3k

A:

Q: 60 6 30 V3/2

A: Topic:- trigonometry ratios

Q: Simplify. 7/16-V54

A:

Q: 2. tox²Sc.

A:

Q: 7.2-2

A: Given:   x y 644 623 493 472 532 492 462 661 565 540   502   549   518

Q: 1/3+4/5=

A:

Q: 2.73-0.94

A: Here we subtract a number in another number.

Q: Number 6.12

A: From part (6.11), Let x be the random variable denote that the amount of snow fall between 1 inch…

Q: 3 33. 3 .2 3.

A:

Q: 4(2w - 5) = 5w + 4 %3D

A: Here we have,  4(2w-5)=5w+4 ................................ (1)

Q: 5x + 8 = 78

A: We Solve the Equation, Find The value of x.  Given Equation is 5x+8= 78.

Q: Let A(x) represent the area bounded by the graph, the horizontal axis, and the vertical lines at t =…

A: