1. Given that F = x?yax – yay, Find $ F· dl where L is shown in figure below b. f, (V × F) · dS where S is the area bounded by L а. 2

Q: Find the area bounded by the following curve and line: y=4/x , y²-4y+2x=5 and the line y=4

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Q: 1. Evaluate : f(4x³ + )dx x+1 2. Find the area bounded by the curves y = x? and y = 2 – x².

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Q: Find the Area bounded by the curves y? = x and x = 2y – y².

A: Draw the graphs of the given curves and mark the intersection area.

Q: Find the area that it encloses

A: The given curve is r=2-sinθ. From figure, it is observes that 0≤θ≤2π. Obtain the area using formula…

Q: The area bounded by the curve y=4- x2 · x-axis and the line is? 16 Ob. 11 Oc. 16 Od. 1 а. 5 3 3 3

A: The graph is shown below:

Q: 2. Find the area bounded by y = x² - 2 and y = 2x + 1.

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Q: Suppose we estimate x2 dx with the Midpoint Rule M2. Let Aj and Az be the areas of the 1st and 2nd…

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Q: The area of the Quadrant I region under the function f(x) = Select one: a. O b. О с. 1 4 I 2 O d.…

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Q: H.W. using the relation r = Vn show that J(x) = COS X %3D

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Q: A) Give f(x)-V-3 find f-*(x) ,x >0 B) : Find the area bounded by the curve y = f(x) =v2x +1 and the…

A: We have to find  A) f-1(x) for f(x) =√(x-3)  B) area bounded by the curve y = √(2x+1) and the lines…

Q: 22. Find the area enclosed by the curve r = v6(1 – sine). A. 7 T sq. units C. 9 n sq. units B. 8 n…

A: The detailed solution of the problem is given in the next step.

Q: Find the area between the curve of y ਆਗੂਆਂ 2 4 = zæ + 2 and the x-axis on the interval [-2, 1].

A: Given that , Now we want to find the area between the curve and the axis  on the interval .

Q: Let f(x) = -a² + 6æ – 5. Estimate the area below the curve y = f(x) and above the x-axis using 100…

A: Let f(x)=-x2+6x-5 To estimate the area below the curve y = f(x) and above the x-axis using 100…

Q: Q1: Find the area bounded by: The curve y=4x-x and the lines y=0, x=1 and x=3.

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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.