Use a change of variables to find the area of the curved rectangle above the x-axis bounded by x=4-y2/16, x=9-y2/36, x=y2/4-1, and x=y2/64-16.

Q: Find the area of rectangular plot if it's length is (5×+8y³) centimeters and it's width is (5×-8y

A: The area, A of a rectangle is given by A=lw, where l is the length and w is the width of the…

Q: What is the area of triangle bounded by the x-axis, the y-axis, and the line y=−4x+4?

A:

Q: The municipal Parks Department is planning a new flower bed outside the city hall. It will be…

A: Given that the dimensions of the rectangular park are 9 m by 6 m. The flower bed will be surrounded…

Q: Evaluate. [ 10.xªtan (2x³ + 3) dx

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Q: ), (4,2), (5,3) b

A: Given as, Here,

Q: The center of an earthquake, called an epicenter, has occurred in a city located at the coordinates…

A: given the center of the earthquake is (1,-4).another point where the earthquake is felt (-3,2)

Q: Find the area of the largest rectangle that can be bounded by the x-axis and the parabola y = a -…

A: The given problem is to find the area of the largest rectangle that can be bounded by x-axis and the…

Q: Find the area of a parallelogram whose adjacent sides are -5/ +k and 61 -3/ -k

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Q: Express 2e3+in6 in rectangular form.

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Q: y= x^4-3x^2+4x-3 find derivativr

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Q: If x^2 + y^2 =14 and x+y=6, find xy.

A: Solution :  Given that   x2 + y2 = 14    ---(1) and  x + y = 6   ---(2)

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.