Find the area under the line y = 9x, between the limits a = 0 and b = 3 a) 32 O b)40.5 c) 42.45 O d) 25.3

Q: Find the volume of the 'ice-cream' that is bounded by x2 + y? + z2 99 and the upper cone z? = 3x2 +…

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Q: Let B be the solid whose base is the circle x^2+y^2=49 and whose vertical cross sections…

A: Given, Circle- x²+y²=49=7² --------equation 1 The equation is of the form x²+y²=r². Therefore, the…

Q: Given a 60 microcoulomb point charge located at the origin, find the total electric flux passing…

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Q: Evaluate , ydV where E is the hemispherical solid region x? + y? + z? 0.

A: x^2+y^2+z^2 <=64, y>=0

Q: Let B be the solid whose base is the circle (x^2) + (y^2) = (4^2)  and whose vertical cross sections…

A: This question is based on application of Integration.

Q: Find the area of region enclosed by x = t – ť², y = t – t", 0 <t < 1 using Green's Theorem.

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Q: Let D be the region in the ry-plane inside the unit circle x? + y? = 1. Evaluate the double integral…

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Q: Find the volume generate by rotating the given region about the specified line. R2 about BC

A: Integrating a small volume element within appropriate limits will result in the complete volume of…

Q: Let R be the annular region Tying between the two circles x + y- x? + y? = 5. Evaluate the integral…

A: The solution follows as :

Q: Evaluate the double integral V1 + 4x² + 4y²dA, where D is the region inside the circle x + y? = 25…

A: We have to find area of the region bounded by the circle given in the first quadrant of the plane.

Q: 27. Find the volume of an ice cream cone bounded by the hemisphere z '8 – x² – y² and the cone z Va2…

A: Given hemisphere z=8-x2-y2 and cone z=x2+y2 The intersection of hemisphere and cone is given by…

Q: Prove that the volume of a segment of height h of a sphere of radius r is V = }nh°(3r – h)

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Q: Find the volume of the part of the ball p < a that lies between the cones o = T/6 and ¢ = T/3. = 10

A: Given ball ρ≤a lies between cones ϕ=π6 and ϕ=π3.

Q: Consider the region D in the xy-plane which is bounded by the following 4 y? = x and y? = 3x.…

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Q: H.W Ennlunte where o is the selid bounded by the Sur faces xサ 0 7 そー

A: Given term is: ∫∫∫Sx2+y2dzdydx and the surfaces are x2+y2=z2, z=0,z=1

Q: The area in the second quadrant of the circle x2 + y2= 2 is revolved about the line y + 1 = 0. What…

A: This problem belong to circle and line section from geometry and we solve this using the second…

Q: Reduce the surface integral ( S A.ds) of a cube of sides parallel to the three perpendicular axes,…

A: Here we can use divergence theorem to reduce the given surface integral. Divergence theorem states…

Q: Compute the volume lying inside the sphere x2 + y? + z2 = 46 but outside of x² + y? = 21.

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Q: Find the area of the part of the cylinder y2 + z2 = 4 in the first octant, cut out by the planes x =…

A: Given. We are given a cylinder in the first octant.. y²+z² = 4 We need to find the volume of the…

Q: Let m be the least possible surface area of a closed circular cylindrical can whose volume is equal…

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Q: Find the volume of the following: SIf xycos yzdV where, G is the rectangular box defined by the…

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Q: The volume of the solid region, in the first octant, that lies below below the surface, z = above…

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Q: Consider the integral a* – y´ dA where Ris the region in the second quadrant bounded e between the…

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Q: Find the volume of the solid whose base is bounded by the circle x2 + y? = 36 and whose cross…

A: Given query is to find the volume of the give solid.

Q: Let m be the least possible surface area of a closed circular cylindrical can whose volume is equal…

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Q: 1. SSR ry? dA, where R is the region in quadrants 1 and 2 bounded by the semicircle of radius 2…

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Q: Evaluate the double integral | (3x – 2y) dA; R is the region enclosed by - R the circle x? + y² = 1.

A: The given region R is a unit circle centered at the origin (0,0). Thus the domain is defined by the…

Q: Find the area of region enclosed by a = t – t, y = t – tº, 0 <t<1 using Green's Theorem.

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Q: Find the Volume r= 2cos 0 , x2+yナ ?= 4.

A: Topic:- volume

Q: Given that R is the region bounded by the curve y = x+3 and line y = x-3. (c) By using the limits in…

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Q: Find the volume generated by rotating the given region about the specified line. R, about BC

A: In this question, we find the volume by rotating the region R1 about the line BC.

Q: Prove that the area bounded by a simple closed curve C is given by | xdy – ydx. Hence, find the area…

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Q: Evaluate the integral R Vr + y² dA, where R is the region inside the upper semicircle of radius 2…

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Q: as Find Hhe voleime of odid generated by revolving tthe region bounded by graphs of y=xe;y 0, and…

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Q: Consider the region D in the xy-plane which is bounded by the following 2 -, Y = 4 y? = x and y' =…

A: Evaluate the integral in two ways. Directly and changing the variables. Last image is the shorter…

Q: Show that the rectangular box (including the top and bottom) withfixed volume V = 27 m3 and smallest…

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

Q: Evaluate the integrul )}EA where f(x,y)=In(x*ッ) is the by the circles x?+y?=9 and the and D cegion…

A: Given information: The function is f(x,y)=lnx2+y2x2+y2 and the region of the integration is x2+y2=9,…

Q: Find the volume of the 'ice-cream' that is bounded by x2 + y2 + z2 = 3 and the upper cone z? = 4x2 +…

A: Let's find.

Q: Compute the volume of the solid above the cone o = , and between the spheres p = 1 and p = 3. Hint:…

A: We have to use spherical co ordinate system

Q: 4. Evaluate f, 2ry dA, where R is the region bounded by y i and

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Q: Evaluate SI, cos (2) dA ,where D is the region bounded by (x, y) D = {- sxs V24 ,0 < y< x²} V8n

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Q: Find the volume.

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Q: Find the volume of the solid bounded by a lune with an area of 36t. The given angle is 25°. C D Q..…

A: To Find: the volume of spherical wedge bounded by lune with an area of 36π, and an angle of 25°.

Q: Find the area of region enclosed by x = t – t, y = t – tº, 0 < t < 1 using Green's Theorem.

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Q: Let C be a simple closed curve bounding a region Din R2. which of the following are equal to the…

A: Let C be a simple closed curve bounding the region D in R2.  So using Green's-Theorem,

Q: The volume of the solid enclosed by the surface z = x/y and the rectangle 2 <x < 4, 1 < y <e² in the…

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Q: Evaluate drdy over the region R which is enclosed by the lines r+ y = ±1 r + y + 2, and r – y = ±1

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Q: Compute the volume lying inside the sphere x? + y? + z? = 37 but outside of x² + y? = 21.

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Q: Find the volume of the solid in the Ist quadrant under the graph of z= f(2, y) = 3- VP+y² and inside…

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