Which of the following is the integral equivalent of the volume of the solid formed by rotating around the y=axis the region bounded by the curve y = x- – 3 and y = 3x + 1 at the left of the y-axis? using cylindrical shells o 22ny (블-Vy+3) dy | oLj 2ay (Vy+3-) dy O L 27 (x) (x² - 3x - 4) dx O , 2nx (-x² + 3x + 4) dx

Q: Find the volume of the solid of revolution formed by rotating about the x-axis each region bounded…

A: Given equations are ƒ(x) = x2, y = 0, x = 1, x = 5. Graph the given region as shown below.

Q: Find the volume of the solid region bounded above by z = 4 – 2x – 2y and above by the triangle…

A: We will find out the required volume.

Q: Find the volume of the solid generated when the region bounded by the curve y=2-(x+1) and the line…

A:

Q: se the method of cylindrical shells to find the volume generated by rotating the region bounded by…

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

Q: se the method of cylindrical shells to find the volume V of the solid obtained by rotating the…

A: Use the method of cylindrical shells to find the volume 'v' of the solid by rotating the region…

Q: Find the volume of the solid generated by revolving about x=0 the region bounded by the given lines…

A:

Q: Using cylindrical shells, the volume of the solid formed by revolving the region bounded by y = 8x',…

A: The given functions y=8x3, y=0, and x=1 The volume of solid formed by the revolution V=∫abAxdx Take…

Q: If the volume of the solid obtain by rotating the region enclosed by the curves y = 2 x2 and y = 0…

A: Integration of curves help us to find volume of curves or area under the curve. It becomes quite…

Q: Find the volume of the solid above the region D={(x,y) : 0s xs V49, 0S ys 49-x2} and between the…

A: volume:  V=∫049∫049-x2(49-y)dydx

Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the…

A: The given equation represents the upper half of the ellipse: Thus the center of the ellipse is at…

Q: 2: Find the volume of the solid that lies below the surface given by z = 10 + x² + 3y² and lies pove…

A: To find the volume of the solid that is bounded by below surfaces. z=10+x2+3y2z=0 xy-planex=1x=0…

Q: Find the volume of the solid generated by revolving the region bounded by y = x² + 2x – 2 an y = x…

A: Given regions: y=x2+2x-2 and y=x Point of intersection will be…

Q: Determine the volume of the solid obtained by the revolution of the region bounded by the curve y =…

A: Volume of revolution

Q: Find the volume of the solid above the region D={(x,y) : 0s xs V71, Os yS 71-x-} and between the…

A:

Q: Find the volume of the solid of revolution formed by rotating about the x-axis each region bounded…

A: Given: f(x)=x+5 , y=0, x=1, x=3

Q: What is the volume of the solid formed when the region bounded by the curve y = V9 – x², x= -3 and x…

A:

Q: Find the volume of the solid region bounded above by z = 4 – 2x – 2y and above by the triangle…

A: We have to find the volume of solid region bounded above by z=4-2x-2y and the triangle  enclosed by…

Q: Find the volume of the Solid generated by revolving the region bounded by x = (1 – y)² , x = 2/ỹ and…

A:

Q: Find the volume of the solid of revolution formed by rotating about the x-axis each region bounded…

A: When a plane area is revolved about any axis say, x or y axis ,it generates a solid having some…

Q: Find the volume of the solid generated by revolving the region bounded by the given curves about the…

A: Given:

Q: Find the volume of the solid of revolution generated by rotating the region bounded by the graphs of…

A: We need to find the volume of the solid of revolution generated by rotating the region bounded by…

Q: Which integral gives the volume of the solid generated by rotating the region enclosed by the curve…

A: We need to find an integral that gives the volume of the solid generated by rotating the region…

Q: Use cylindrical shells to find the volume of the solid obtained by rotating the region bounded on…

A:

Q: Find the volume of the solid generated by revolving about x=0 the region bounded by the given lines…

A: Solve by volume revolution

Q: Let S be the solid of revolution obtained by revolving about the z-axis the bounded region Renclosed…

A:

Q: Set up the integral that uses the method of cylindrical shells to find the volume V of the solid…

A: Given query is to find the integral for the volume of the solid generated.

Q: Determine the volume of the solid obtained by the revolution of the region bounded by the curve y =…

A:

Q: Find the volume of the solid generated by revolving the area bounded by x- y² + 4y-4 0 and x- y-4 0…

A:

Q: Find the volume of the Solid generated by revolving the region bounded by y = Jx and the lines x =…

A:

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

A: Given: The solid generated by revolving the region bounded by y=2x-x2 and y=x about the line x=-1.

Q: Find the volume of solid generated by revolving the region bounded by the curve y=4/x' and the lines…

A: Disclaimer:  “Since you have posted a question with multiple sub-parts, we will solve the first…

Q: The volume of the solid obtained by rotating the region bounded by y = x?, y = 4x, about the line a…

A:

Q: Find the volume of the solid of revolution formed by rotating about the x-axis each region bounded…

A: The graph of region bounded by the curves f(x) = 2ex, y=0, x=-2 and x = 1 is given below:

Q: A region bounded by f(y) = √√√y + 1, y = 1, y = 4, and x = 0 is shown below. Find the volume of the…

A:

Q: 6) Use double integral to find the volume of the solid bounded above by the paraboloid 9x² + y²,…

A: We can find the volume of the solid by using double integral .

Q: Find the volume of the solid of revolution formed by rotating about the x-axis each region bounded…

A: Given that the region is bounded by y=x2,  y=0,  x=1  and x=5. Sketch the region as shown below.

Q: se the method of cylindrical shells to find the volume V generated by rotating the region bounded by…

A: Ans 136 Pi/5

Q: Find the volume of the solid generated by revolving the region R bounded by the graphs of tE the…

A:

Q: The volume of the solid obtained by rotating the region enclosed by y = x², x = y? about the linex =…

A: we will solve the problem using washers method.

Q: Consider the solid obtained by revolving the region bounded by x² + (y – 7)² = 25 about the x-axis.…

A: Given that the solid obtained by revolving the region bounded by x2+(y-7)2=25 about the x-axis.

Q: Find the volume of the solid bounded above by the cylinder y = x2 and below by the region enclosed…

A:

Q: Find the volume of the solid generated by revolving 4 the two x² the area bounded by the curve y =…

A: The given curve is; y= 4/x2 the two lines are y=1 and y=4 about the y-axis.

Q: 2. Find the volume of the solid generated by revolving about the line x = -2 the region bounded by…

A:

Q: The volume of the solid obtained by rotating the region enclosed by y = 1/x³, y = 0, x = 3, x = 4…

A:

Q: 2. Find the volume V of the solid of revolution generated by revolving the region bounded by the…

A: Given that y=2x-2x2  Find the volume about x-axis Also the given line is x=2

Q: Find the volume of the solid generated by revolving the region about the y-axis. 3 The region in the…

A:

Q: What is the volume of the solid generated by revolving the region bounded by y = x², y = 0 and x = 2…

A: Please see the answer below.

Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the…

A:

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

A:

Q: Find the volume of the solid generated when the area bounded by the given curves and lines is…

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.