Let B be the region in the first octant inside both x? + y + z? = 1 and x² + y² . a) Find the triple integral 3zdV. В b) Find the triple integral 2ydV. B c) If possible, find a value of a so that I/| (az + 3y)dV = 1. || В

Q: Find the area of the shaded region. y-2 C4, 2) O4, 2 A) 2 (B) n-2 D) n

A: The area of the region can be found by the following formula  Area =∫abydx Area =∫ab|f(x)-g(x)|dx…

Q: Evaluate ffRrdA, where R is the region bounded by y -r + I, y=-I, y=0 and y 1 as in the picture.

A:

Q: Find the area bounded by the arc square root x + square root y = 7, the x axis, and the line joining…

A: Given curves are                                                   1x+y=7, y=0, points (16, 9) &…

Q: If F(x, y, z) = 10yzi + 10xzj + 10xyk, find div F and curl F. div F =

A:

Q: Q1) Find plane area bounded by y = 2,y = 6 – x, and y = 8 - 3x using double %3D

A:

Q: X= (y-3)2 and X= 16 about the X=- 5

A: Given curves: x=y-32 and x=16 Revolved around: x=-5 To find: Volume of the object formed by the…

Q: Find the area of the surface S defined by z = xy and x² + y² ≤ 3. (Use syntax like 2*pi/3)

A: (.)  Given ,  Area of the surface S defined by z=xy and x2+y2≤3 .   If  z=f(x,y) ∀ (x,y)∈R  the…

Q: Determine the area bounded by: y2-12y-8x+28=0; and x2-4x+4y-20=0

A: The given equations: This can be rewritten as, To find the area bounded by the above equations:…

Q: Q4A) Find area bounded by y = 0, y = 1-x²,x= 0 and x = 1. B)Is w=zx¹ analytical function or not? 2 2…

A:

Q: Find the area of the shaded region given below. y = √√√=x+4 y = √√x + 4 neg y = x² + 4 x = y² -6y +8…

A:

Q: Evaluate. where G is a solid that lies in the first octant bounded by x^2 + y^2 = 3z and z = 3.

A:

Q: Determine the area of the region enclosed by the Y-2x = -1 and 4 = x ² = 4x+4. Do not simplity…

A:

Q: 3) Let R be the region in Q1 bounded by the graphs of these equations: y =16-x²,y=-4x+16 Sketch R on…

A:

Q: Which integral corresponds to the area of the shaded region? The parabola is y = x? –1 while the…

A: Given query is to find the the integral for the area of shaded region.

Q: Ive the area of the region bounded by y=x²– 3x+ 12 and by y=18+x-x? A) -199 B 199/3 c) 63 D -10/3

A: Given query is to find the area bounded by the region.

Q: Find tu are and centrord banded by 2 X ニ 4-4y 4-y Graph. こ

A: Given boundary curves1. x = 4-y2  ⇒ y=±x-42. x = 4-4y  ⇒ y= 144-xPlot the curves, get the…

Q: Evaluate where D is the region bounded by the semicircle x = /4– y² and the y-axis.

A:

Q: Find the volume V of the region appearing between the two surfaces z = x² + y² and z = 8 - x² - y².…

A:

Q: Set up the triple integral that will give the following: the volume of the solid B that lies above…

A:

Q: a) value of a. b) area of the shaded region. c) volume generated, in terms of a when the region…

A: In this question, we have to find the intersection point between two curves  and in the second part…

Q: Set up the triple integral that will give the following: the volume of R using cylindrical…

A: To set up the triple integral that will give the volume of the below solid R using cylindrical…

Q: Q) Evaluate. the integral below x²4ux (7x-35-x²5x²)(xzux+u)

A: