Let S be the portion of the cylinder z = 1 − x2, in the first octant and between the planes y = 0 and y = ax, where a is a positive real constant.   The value of a for which Area (S) = 53/2−1 is:

Q: Given If G is the solid bounded byz =6-y, z=y-10 and y=x2 where dV = dzdydr. Find the lower and…

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Q: 1) Find the volume of the prism whose base is the triangle in the xy-plane bounded by the x-axis and…

A: To find the volume of the prism described we just need to evaluate the given double integral…

Q: Evaluate the triple integral. 3xy dV, where E is bounded by the parabolic cylinders y = x² and x =…

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Q: Given a solid bounded by f(x,y) = 3x² + 2yª, xy- plane, x = 3, x = 12, y = 6 and y = 16. If the…

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Q: The volume of the solid E bounded by the cylinders 2 + y? = 1 and x2 + y? = 4, and the planes z = 0…

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Q: 24 of 34 Find the volume of the solid generated by revolving the area bounded by the given curves…

A: I use disc method to find volume

Q: Find the value(s) of c such that the area of the region 2 bounded by the parabolae y = x² – c² and y…

A: see below the answer

Q: tind the value of the consrant (min) that makes the D-E j X dx -CyfmX) dy so (Homogeneous, exact,…

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Q: Let f(x) = log(x + 1), g(x) = 10-x, and R be the region bounded by the graphs of f and g, as shown…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the volume of the solid bounded by z= - y, the xy-plane, and r=4 cos 0.

A: The answer is 8.33

Q: The graph of y = f(x) between the lines x = a and x = b is rotated around the line y = 3 to form a…

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Q: The double integral ff 2xycosydA over the rectangular region R = {(x,y) E R², 0<x<1 and 0 <y<n} is…

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Q: The mass of the solid occupying the hemisphere x²+y²+z²0, and having density 6(x.y,z)=3 +…

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Q: Q#1. Set up a formula using triple integral to find the volume of the solid enclosed between the…

A: We have to set up a formula using triple integral to find the volume of the solid enclosed between…

Q: Evaluate the integral [[[var !!! y² dv where G is the solid in the first octant that lies below the…

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Q: The double integral Jf 2xycosydA over the rectangular region R= {(x, y) E R2, 0<x<1 and 0 < y<n} is…

A: We have to evaluate the double integral ∬2xycosydA over the rectangular region R. Given that…

Q: The volume of the solid generated by revolving the regie line x = 3 is (A) 27 (3+ x)(2x – x²) dx (В)…

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Q: 9. Fill in the items needed to numerically integrate a function over a volume: bu I = ,f(x, y, z)dV…

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Q: Find the positive constant A given that the volume of the solid bounded by the paraboloid, x2 + y2…

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Q: Find by double integration the volume of the finite solid lying underneath the graph f(x, y) = x² –…

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Q: The value of the triple integral II| 2x² dV where E is the region inside both x? + y? + z? = 36 and…

A: Solution:-

Q: The solid S is obtained by rotating the region enclosed by y = f(x) > 0, x = 5 + 5e! 5+ 5e17 and a =…

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Q: Let C denote the solid that is = 0, • bounded above by z = e-2(x² +y² ), and • lying within the…

A: To find the volume of the solid that is bounded by the below surfaces. z=e−2x2+y2 z=0 x2+y2=4

Q: 3. Find the volume of the given solid. a. Under the paraboloid z = x² +y? and above the region…

A: Given: The solid is under the paraboloid z=x2+y2 and above the region bounded by y=x2 and x=y2.

Q: Let A be the region bounded by y = 8x 3(1−x) and the x-axis between x= 0 and x= 1. Find the solid…

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Q: Evaluate the integral, where E is enclosed by the paraboloid  z = 4 + x2 + y2,  the cylinder  x2 +…

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Q: 7. Find the volume obtained by revolving about 0X the area under the catenary y = (*+ e¯), from z =…

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Q: Given that E is the solid bounded by four planes x=0, y=0, z=0 and x+y+z=1, then the value of the…

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Q: 3Af F=x1-yj+(z- 1) k, V is the volume of the cylinder bounded by z = 0, z = 1 and x +y = a° and S is…

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Q: aluate the triple integral zdV, where E is bounded by the cylinder y? + z? = 9 and the planes a = 0,…

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Q: The region under the curve y = x2 x between 1 and x 3 is revolved about the line x = 3. Using the…

A: When we revolve around the x = 3 axis, then then the radius of the shell will be: R = 3 - x, height…

Q: 1 Find the volume generated when the area bounded by y=√√x and y=-x is rotated around the x-axis 2 A…

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Q: 5. Let S be the solid in the first octant bounded by the cylinders x² + y? = 4 and x² + z² = 4. (b)…

A: Given- Let S be the solid in the first octant bounded by the cylinders x2+y2=4, and x2+z2=4. To…

Q: let m be the region in the first quadrant bounded by y=sin(pix/2) and y=x^2. what is the volume of…

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Q: The double integral ſſ 2xycosydA over the rectangular region R = {(x,y) E R², 0 <x<1 and 0 < y< n}…

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Q: Evaluate the triple integral. III. 7z dv, where E is bounded by the cylinder y2 + z² = 9 and the…

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Q: Evaluate the triple integral z dV, where E is bounded by the cylinder y? + z2 E 4 and the planes x…

A: To Evaluate: The triple integral ∫ ∫ ∫ E z dV  where E is bounded by the cylinder y2 + z2 = 4  and…

Q: Find the constant k > 0 such that the volume of the region lying inside the sphere x2 + y2 + z2 = a2…

A: Given that,k&gt;0 is a constant such that the volume of the region lying inside thesphere…

Q: Evaluate the triple integral. 2z dv, where E is bounded by the cylinder y? +z? = 9 and the planes x…

A: According to the given information, it is required to evaluate the triple integral.

Q: Evaluate the 2d integral Sla ydædy, where the region 2 is defined N:= {(x, y) E R² : 0 < x < 7, sin…

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Q: ind the volume of the solid generated by revolving the region bounded by = x² +1 and y =x+4 about…

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Q: Let R be the region bounded by f(0) = sin 6 cos3/2 0 and the a-axis for 0< <T/2. Use the Disk/Washer…

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Q: Define R as the region bounded by the functions f(x) = 2 and g(x) = e¯i between x = 0 and æ = 2. If…

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Q: Given f(x, y) = 4x³ + 6xy². a) Draw the region that is the base (or footprint) the surface, b) Setup…

A: The region is formed by the rectangle represented by the line: x=1, x=3, y=-2, y=1  (See the image…

Q: The graph of y = f(x) between the lines a = a and æ = b is rotated around the line y = 2 to form a…

A: Proceed as shown below...

Q: The volume of the solid E bounded by the cylinder x + y² = 1, and the planes z = 1 and z = 3 in the…

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Q: Let D be the solid whose base lies on the xy plane and is bounded by the graphs of y = 2x and y = 3…

A: To find the point where the two functions intersect, equate the two.   Cross-sectional area of the…

Q: Let the region R be the area enclosed by x = + 1 and 2 Vy + 1. Find the volume of the solid…

A: The curves are x=y2+1 and x=y+1 The point of intersections are…

Q: The volume of the solid E bounded by the cylinders a2 + y? = 1 and x2 + y? = 4, and the planes z = 0…

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Q: Find the absolute maximum and minimum Of the function f(x, y) = x + Y on the elliptic region {(x, y)…

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