10. Use a definite integral to find the exact area enclosed by the x-axis and the parametric curve = v2(t3 + 1), y = 2t – t2. x

Q: Find the area of the surface swept out by revolving the para- metric curve x = 5 cost + 5t sin t y =…

A: Area under curve.

Q: Find the area of the surface generated by revolving the curve 1 V1 + eb", 5x 0 < x < 2 around the…

A:

Q: The area of the surface obtained by rotating the curve x = 1sys7 about the x-axis is

A: Definition used -              Area of the surface obtained by rotating the curve x=g(y) about…

Q: 1 Find the area of the surface obtained by rotating the curve y = In(1 – x²), 0 < x <. about the

A:

Q: Find the surface area for the object obtained by rotating y = 7x + 2 about the x-axis over the…

A: The object is obtained by rotating about the x-axis over the interval .We have to find the surface…

Q: Find : ( 39 - Sincm) dx +(2x*) dy when C is the boundary of the limited area by curvess y= e* and in…

A: Given that I=∫c3y-sin x dx+2x2 dy                                   ……(1)   Boundary is given as…

Q: Find the area of the surface obtained by rotating the curve y=sqrt(4x) from x=0 to x=6 about the…

A:

Q: Calculate the surface area if the curve y = 3sqrt(x) is rotated about the x-axis.

A:

Q: Find the area of the surface obtained by rotating the curve y = √5x from x = 0 to = 4 about the…

A:

Q: The area of the surface obtained by rotating the curve y = 17 x +1, 0SXS 34 about the x-axis is

A: The solution are next step...

Q: What is the moment of inertia of this area about the line y = -10 ?

A:

Q: Determine the surface area generated when a portion of the curve in the 1st quadrant of y? = 4(x² –…

A: Given: y2=4x2-a2 Portion of the curve in the 1st quadrant is revolved about x=0 (y-axis) from y=0 to…

Q: A plane area is bounded in the first quadrant by the curves y² = -16 (x-4), the line 8x-15y = 0, and…

A: Given the curve is y2=-16x-4 and the line 8x-15y=0 and x-axis. We have to find the moment of inertia…

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.