Use cylindrical coordinates to calculate the triple integral [ f(x, y, z) dV for the function f(x, y, z) = 1156 ²√ x² + y² and the region x² + y² ≤ z ≤ 34 − (x² + y²). (Express numbers in exact form. Use symbolic notation and fractions where needed.)

Q: b) Express the area of the pool, A in terms of I and r. c) Hence, or otherwise show that A = -² +…

A:

Q: Apply Green's Theorem to evaluate the integral (4y² dx + 4x² dy), where C is the triangle bounded by…

A:

Q: Apply Green's Theorem to evaluate the integral $(2y² dx + 2x² dy), where C is the triangle bounded…

A:

Q: 7) Find the area under the parabola y = x² – 2x +2, above the x-axis and between x = 0 and x = 1.

A:

Q: Evaluate the line integral f3y² dx + z² dy + (16 - x²) dz over the quarter of the circle of radius 4…

A: Kindly refer to Step 2 for the solution.

Q: Apply Green's Theorem to evaluate the integral. $(4y + x) +x)dx + (y + x)dy C: The circle (x-3)² +…

A:

Q: hat is the area of the region bounded by the line x = 4 and the curve x³ = x² + 2xy - y² = 0. ht:…

A:

Q: f(x) = √√/x = -²x³12 about the x-axis for 1 ≤ x ≤ 3. .3/2

A:

Q: 9. Let D be an integral domain such that (x + 1)² = x²+ 1 in D[x]. Char D = а) 0 b) 1 c) 2 d) 3 O a)…

A:

Q: Find the surface area for the object obtained by rotating y = 7x + 2 about the x-axis over the…

A: The object is obtained by rotating about the x-axis over the interval .We have to find the surface…

Q: 2. Let D be the parallelogram bounded by the lines x+3y = 5, –x + y = 3, –x + y = 2, and x + 3y = 0.…

A: Let us consider the integral I=∫∫Df(x,y) dydx where D is the region in xy-coordinate  To make the…

Q: Apply Green's Theorem to evaluate the integral. (4y + x)dx + (y + 3x)dy C: The circle (x-6)² + (y -…

A: We have to find the value of integralFor this we using green theoremThe green theorem says that

Q: x=√4−y, y=0, and y=x+2. a. Sketch the region enclosed by the curves.  b. Find the area of the…

A:

Q: 3. Find the area of the cardioids region shared by ri 7(1- sin 0) and r2 = 7(1+sin 0). A 7(1 Sint) B…

A: The given curves are:  r1=71-sinθr2=71+sinθ To find the intersecting points,…

Q: Exer.) Express and evaluate the integral (x+y) dv E as an iterated integral for the given solid…

A: Given:

Q: Use calculus to show that the maximum possible area of a triangle with one vertex at (0, 0) and the…

A:

Q: ). Explain how we get the Cylinder by equivalent relation.

A: Please check the next step for details

Q: For #1 and =2, find the area of the shaded region. No calculator, show all work 1) (1.1) 2) +y=2

A:

Q: 1. SET UPANISTEGRAL REPRESGNTATIOL OF THE AREA OF THE TRIANGLE BELOUU (a.2) (3,1) (0.0)

A: To set up an integral representation of the area of the triangle below