Let a)I be a constont ancl let e be the reafon bouncleo by y=ltx? ond y=1E x +36. Finc the volume of solicl generateol by revolving the region 2asout the line xe-a,

Q: Write the transformation matrix for a R2→ℝ2 linear transformation that rotates points 150∘ above the…

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Q: nx+2sinx Q2.a) lim sin (-)+ sec 3+x b) Find the volume generated by revolving the region enclosed…

A: Limits and volume of revolution is

Q: Rx+2sinx Q2.a) lim sin (). sec (in 3+x

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

Q: Find the Volume the Colid obtained by rotating the vegion enclosed about linie 4=0 Using the metned…

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Q: Find the volume generated by rotating the given region about the specified line. y 0.5- R₁ R₂ y=x²…

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Q: Find the volume generated by rotating the region bounded by y = e¯ , y = 0 , x = - 1, x = 0 about…

A: A region is bounded by y=e-x, y=0, x=-1 and x=0, about the line x=2. The objective is to find the…

Q: Find the volume V which lies inside the sphere x + y' +(z – 5)² = 25 and outside the sphere x? + y?…

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Q: A $ 100 deposit is made into a college fund at the beginning of each month for 10 years. The fund…

A: Consider the given information. The deposit amount is $100. The rate is 9% and the time is 10 years.…

Q: Solve the initial value problem below using the method of Laplace transforms. y" - 4y' - 12y = 0,…

A: Given equation is: y"-4y'-12y=0 ,y(0)=1,y'(0)=38 We have to find the value of y(x)

Q: Q3) Find volume of body from below z = x2 + y? and above z = 1.

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Q: Consider the solid E bounded by z = 10 - 2x - y and situated in the first octant. Find its volume.

A: Here we have to find the Volume of the solid E bounded by the plane z=10-2x-y…

Q: Find the volume of the rotating body formed by rotating the region between the y=f(x) curve, the…

A: We have to find the volume

Q: Find the volume enclosed between the two surface :z x + y and z=3

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Q: The Valume of the Kotuting bady resuling from the Yotution of the region lacated in the first…

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

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.