6. Find the volume of a solid whose base is the region bounded by y = 4 – x² and the x-axis and whose vertical cross sections (perpendicular to the x-axis) are squares.

Q: 2. Consider the first quadrant region bounded by y² = x, the x-axis and x = 4. Find the volume when…

A: Disclaimer-Since you have asked multiple questions, we will solve the first question for you.  If…

Q: 2. Find the volume generated by revolving about the y-axis, the area bounded by x² + y² = a² and x+y…

A: The bounded region: Green colored    To find: The volume of revolution around y-axis of the bounded…

Q: Let M be the region in the first quadrant bounded by the graph of y=3x+2, the graph of y=x+2, and…

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Q: 5. Find the volume of the solid obtained by rotating about the x - axis of the region bounded by y =…

A: We have to compute the volume of the solid generated by revolving the region bounded by the curve…

Q: Let A1 be the region bounded by y = 5x (1−x) 2 and the x-axis between x= 0 and x= 1. Find the…

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Q: 7. Find the volume of the solid obtained by rotating the region under the graph of f (x) = 9 – x2…

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Q: 1) Find the volume of the solid cut from the first octant by the surface z=4-x2-y.

A: As per our guidelines we are supposed to answer only first question. Kindly repost other question as…

Q: 2. Find the volume of the region bounded by y = vx and y 4x rotated about the x-axis.

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Q: Find the volume of the region between the cylinders x² + y² = 36 and x? + z2 = 36.

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Q: 27. Find the volume generated by rotating the area bounded by y = x² + x, x = 1, x = 4, and the…

A: Given that: y=x2+x,   x=1,  x=4   and   the   x-axis To sketch the graph,

Q: What is the volume of the solid whose 1 30 cross-sections are squares perpendicular to the x-axis…

A: Given: The region bounded by the curves are: y=x and y=x The cross-sections are squares…

Q: 4. Find the volume of the solid obtained by rotating about the y-axis the region bounded by y = 2x2…

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Q: 4. Find the volume of the region bounded by y = -x+1, x = 0 and y = 0 revolved about the x-axis.

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Q: Find the volume of the solid generated when the region between the graphs of the equations f(x) + x…

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Q: Suppose that RR is the finite region bounded by  y=x, y=x+4, x=0, and x=2. Find the exact value of…

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Q: 4.Find the volume of the solid that is obtained by rotating the region bounded by y = /x +1, y = Vx…

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Q: 1) Calculate the volume of the solid created by rotating the region bounded by y = x² +1 y = -x + 3…

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Q: 3. If the region bounded by the curves y =x, y=0, and x =9 is the base of a solid, and cross…

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Q: 1. Calculate the volume bounded by y = x², y = 0 and x = 2 rotated about the specified line, using…

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Q: Define Q as the region bounded by the functions f(x)=x^2/9 and x=2 in the first quadrant between y=2…

A: Use the washer's method to solve the problem. The volume of the solid is given by V=π∫cdfy2-gy2dy.

Q: Find the volume of the solid whose base is the region in the first quadrant bounded by y = x°, y =…

A: We have to determine volumes of solid

Q: 9. Find the volume of the solid obtained by rotating the region bounded by y = Vx. x 0, and x = 4…

A: To find: The volume of the solid obtain by rotating the region bounded by y=x, x=0 and x=4 about the…

Q: 4. Find the volume of the region bounded by y = - x+1, x = 0 and y = 0 revolved about the x-axis.

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Q: 2. Find the volume of the solid whose base is the region bounded between the curve y=x² and the…

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Q: 3. Find the volume of the solid formed by y = √√4sin(x) bounded by x = 0 revolved about the x axis…

A: According to the question we need to find out the volume of revolution of the curve.

Q: The volume of the region bounded by x² + y² + z2 =1 is

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Q: What is the volume of the solid generated when the region bounded by the graph of x = √y - 2 and the…

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Q: 4. Set up a (sum of) definite integral(s) that is equal to the volume of the solid whose base is R…

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Q: 2. Find the volume of the solid generated by revolving about the x – axis the region bounded by the…

A: Topic = Volume

Q: 4. Determine the volume of the solid obtained by rotating the region bounded by y = x² - 4x + 5, x…

A: as per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: find the volume (in units 3) generated when the region between the curves is rotated around the…

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Q: 4) Find the volume of a solid generated by revolving about the x- axis the region bounded by y = x2…

A: We find the volume of a solid generated by revolving about the x- axis the region bounded by y = x2…

Q: 3. Find the volume of the solid that results when the region enclosed by the curves x = = y² and x =…

A: If the region bounded by x=f(y) and x=g(y) on [ a, b], where f(y)≥g(y)is rotated about the y‐axis,…

Q: Find the volume of the solid obtained if the region bounded by the graphs of y = \x , y =0, and x=9…

A: Hello. Since your question has multiple parts, we will solve the first question for you. If you want…

Q: 4. Compute for the volume of the solid formed by rotating the shaded area about the x- axis. * 30-…

A: Given: f(x)=25-x2

Q: Find the volume of the solid whose base is the region bounded between the curves y = x and y = x²,…

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Q: Let B be the region in the x y plane enclosed by y = 3−x2 and the x-axis. Let S be the solid shape…

A: let B be the region in x-yplane enclosed by y=3-x2 and the x-axis. S be the solid with base B and…

Q: (4) Find the volume of the solid obtained by rotating the region bounded by y y=√x about the y = 1.…

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Q: 9) Find the volume of the region bounded by y = x + 1 x +1' Y = 0, x = 0, and у %3D0, х%3D x = 4…

A: The formula for the washer method around the x-axis is V=π∫abf(x)2-g(x)2dx where f(x) is the top…

Q: 12. Consider the region R bounded by the line y = 37 – 7x and the parabola y = 27 – x² . %3D Find…

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Q: 5. Find the volume of generated by rotating the region bounded by x = 4y – y? and x = 0 (a) about…

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Q: 1. Use your preferred method to calculate the volume of the solid obtained by revolving the region…

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Q: Find the exact volume of the solid whose region is bounded by y = 2 a + 2, y = 0, x = 3 and x =…

A: Given data : y=2x+2 , y=0x=3 , x=4

Q: 4. Find the volume of the solid generated by revolving the region bounded by y = x 2 + 2 and y = x +…

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Q: 1. Find the volume of the solid generated by revolving the region bounded by the parabola x =y? and…

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Q: Calculate the volume of the infinite solid obtained by rotating the region under y = (x2 + 1) −2 for…

A: Use shell method and find the volume.

Q: 5. Find the volume generated by the areas bounded by the straight line y = x, between y = 0 and x =…

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Q: 4. Find the volume of the solid obtained by rotating the region bounded by y = e", y = 0, x = -1, x…

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Q: Find the volume of the solid bounded above by the graph of x2 + y2 +z2 = 5 and below by the graph of…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…