Use the slice method to find the volume of the solid:  the base is defined by the parabola y = 4-x^2 in the first quadrant.   The slices are squares perpendicular to the xy-plane and perpendicular to the x-axis

Q: Find the volume of the solid that results when the region enclosed by the curves y = -x and x = 2y“…

A: The two functions are as follows:                    y1=14x2y2=x2 The points of intersection are the…

Q: Sketch the region enclosed by the curves y = 8-a2 and y = 2x in the first quadrant. Find the volume…

A: First of all we find the intersection point of the curves y=8-x2   and  y=2x , So 8-x2=2x ⇒…

Q: y = 9x² and y = 0 about x = -4

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Find the volume of the solid obtained by rotating the region bounded by the curves y=√2x, y=x^2/2,…

A: Given curves, y=2xy=x22 Using the washer method: Formula for the volume of the solid obtained by…

Q: Evaluate the volume of the solid generated by revolving the plane region about an axis. Show your…

A: This question can be solved using the concept of volume of the solid generated by revolving the…

Q: Find the volume of the solid formed by rotating the region bounded by y = 5 – 2x, y =x² and x > 0,…

A:

Q: The region in the first quadrant that is enclosed by the x-axis, the curve y = 5/{x√(5 - x)}, and…

A: We first sketch the region using a graphing calculator

Q: Find the volume of the solid whose base is bounded by the circle x2 + y2 = 16 and whose cross…

A:

Q: Find the volume of the solid whose base is the semicircle y = /25 – x² where –5 < x < 5 and the…

A: Given the base of the solidy=25-x2 , y&gt;0The intersection of the base with the x-axis :Put y =…

Q: ) Find the volume of the solid whose base is the region in the first quadrant bounded by y = x5, y =…

A: Here, the cross-sections perpendicular to the x-axis are semicircles whose base span from y=x5 &amp;…

Q: Sketch the region enclosed by the curves y = 8-x² and y = 2x in the first quadrant. Find the volume…

A:

Q: Determine the volume of the solid obtained by rotating the region bounded by the curves y = x2 – 6x…

A: We shall use shell method to calculate the volume:

Q: Determine the volume of the solid obtained by rotating the portion of the region bounded by…

A: First we have to plot the given region.

Q: Evaluate the volume of the solid generated by revolving the plane region about an axis. Show the…

A:

Q: Find the volume of the solid formed by rotating the region inside the first quadrant enclosed by y =…

A:

Q: Use the washer method to determine the volume of the solid obtained by rotating the region bounded…

A: Given solid is the region bounded between y=10-6x+x2, y=10+6x-x2, x=1 &amp; x=5. To find the volume…

Q: Use the Shell Method to compute the volume of the solids obtained by rotating the region enclosed by…

A: We have to use the Shell Method to compute the volume of the solids obtained by rotating the region…

Q: Find the volume of the solid whose base is in the first and second quadrants bounded by y=16−4x2 and…

A:

Q: Find the volume of the solid whose base is in the first and second quadrant(s) bounded by y = 32 –…

A:

Q: Find the volume of the solid formed by revolving the region bounded by the curves y = 3x²,x = 0, and…

A: Given : Curves y = 3x2, x = 0 and y = 3   To find : Volume of solid formed by revolving the region…

Q: The region in the first quadrant that is enclosed by the x-axis and the curve y = 3xsqrt(1 - x) is…

A: Given:

Q: find the volume of the solid that results when the region enclosed by the curves y=(9-(x^2),y=0)

A: To find: The volume of solid generated by curves y=9-x2, y=0 Formula used: The volume of solid…

Q: Find the volume of the solid generated by revolving the region bounded by the y = 2x - x2 and y = 0…

A: Find out the volume of the solid generated by revolving the region by the y=2x-x2 and y=0 about the…

Q: The base of a solid is the region in the first quadrant bounded by the graph of y=2x-x^2 and the…

A: *to find:- Volume of solid.

Q: Find the volume of the solid generated by revolving the region bounded by the y = x2 and y=6x-2x2…

A: Given that y = x2 and y = 6x- 2x2 and we find volume about the y-axis and plot the graph. Here i…

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

A:

Q: Find the volume of the solid obtained by rotating the region across the x-axis.

A: We have to find the volume of the solid obtained by revolution the region bounded by : f(x)=ex3+e2x…

Q: Find the volume of the solid whose base is the region |x|+|y|≤4 and whose vertical cross sections…

A:

Q: Find the volume of the solid generated when the area bounded by the curve y = square root of x,…

A: Find the volume of the solid generated when the area bounded by the curve y=x, y-axis and the line…

Q: Evaluate the volume of the solid generated by revolving the plane region about an axis. Show the…

A:

Q: Find the volume of the solid formed by rotating the region inside the first quadrant enclosed by y=…

A: Given: y=x4 and y=27x

Q: Use the general slicing method to find the volume of the following solid. The solid whose base is…

A: Given that the base of the solid is the region in the first quadrant bounded by the curve y=3-x and…

Q: The base of a solid is the region in the first quadrant bounded by the curve y = Vsinx for 0SxST. If…

A:

Q: Evaluate the volume of the solid generated by revolving the plane region about an axis. Show your…

A:

Q: Find the volume of the Solid generated by revolving the region bounded by y = -2x² and y = x² – 3 ,…

A:

Q: Find the volume formed by rotating the region enclosed by: y = x³ + 1, the y-axis, and y = 9 about…

A: We will use the disk method to evaluate the volume of the solid of revolution.

Q: Find the volume of the solid generated by revolving the region bounded by the y = x?and y = 6x– 2x2…

A:

Q: Find the volume of the solid generated by revolving the region bounded by the y2-x2= 1, y = 2 about…

A:

Q: Find the volume of the solid. y=9-x2, y=0, about the x-axis

A: The given solid is bounded between the curve y=9-x2, y=0,  rotating about the x-axis. Volume of the…

Q: Find the volume of the solid whose base is the region |x| + |y| ≤ 1 and whose vertical cross…

A:

Q: Find the volume of the solid generated when the region enclosed by y = sqrt(2x + 8), y = x, x = 0 is…

A: Given :     To find the volume of the solid.

Q: Find the volume of the solid generated by revolving the region bounded by the parabola y = 2x2 and…

A:

Q: Find the volume of the solid obtained when the region bounded by the line y = 2x, the line x = 3,…

A:

Q: Find the volume of the solid obtained by rotating the region enclosed by the curves y =7x2, y = 7x…

A:

Q: Calculate the volume of the solid obtained by rotating the region bounded by the parabola 4py = x²…

A: For the solution follow the next steps.

Q: Find the volume of the solid formed by revolving the region bounded by the graphs of y=x^2+3 and…

A: The Washer Method : The volume of the solid generated by revolving about the x-axis a region between…

Q: Determine the volume of the solid of revolution when the region enclosed by the x  – axis, the curve…

A: Given, the region is bounded by the x-axis, the curve y=x12 and the line x=3,  Drawing the graph of…

Q: Find the volume of the solid obtained by rotation of the region enclosed by the graphs of y y = 0,…

A:

Q: The region in the first quadrant that is enclosed by the x-axis and the curve y = 3x√(1 - x) is…

A:

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.