Find the area of the region that is bounded by the curve „2 - 9 cin 2 A, where r > 0 and 0 3 03 2 OA. 45 2 63 C. 2 O D. 18 O E. 9

Q: ot) Evaluate the integral 9 L₁ (1x) — 4) da (|x|- dx - -7 using the net area of a region. Give the…

A: Here we have given an integral:

Q: 2/ determine the area of the region enclosed between the curves x= 0.sy-3 and y=x-1? ans/ 18

A: Topic- Application of Integration

Q: Determine the area bounded by y = x + 1 and y=1-x

A: If   x=fy be a continuous function of  y on a,b,then the area bounded by the curve x=fy and the…

Q: Find the area between = 0, y = e- * and y = ex through the interval [-2,1].

A: The equation of curves are: y=e-x ; y=ex The interval is -2,1.

Q: The paper cup shown in the attached document has radius R2=1.5R1, height (h), volume V=716 cm^3,and…

A: Given that :R2 = 1.5 R1Hence including R2 in the volume formula or equation

Q: 6.(. Find the area of the region enclosed by the curves y = x² +1 and y = x +3.

A: I am solving this in step 2

Q: Find the area bounded by the region y = 2x + 2 and the lines y = 1, y = 2

A:

Q: Find the area of the region bounded by one loop of the curve y"(1 - у?)

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Q: The area of the region bounded by the graphs of y = sinx, y = x+1, and the y - axis is 01+ ³…

A:

Q: Determine the area bounded by f(x)=x²-X and x-axis. A 1 4 unit² B unit² (C) unit² D ~/m 6 unit²

A:

Q: Q5) (Definite Integral) curve y = x - 2, the line y = x, and the x-axis. Find the area of the region…

A:

Q: 2- Region enclosed by the cardiaid (r=\- Sin@)in 1-st quadrant.

A:

Q: What is the area bounded by the curve y² x – 4 = 0? А. 29/3 В. 30/3 С. 31/3 = x and the line %3D -…

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Q: Calculate the area between the areas of the black lines.

A: Given figure is,

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.