Find the area of the finite region bounded by the curve y = 12 + x - x2 and the line: y = x + 3.

Q: Q3:B/ Find the areas of the regions enclosed by the line and the curve y = x* – 4x? + 4 and y = x?

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Q: Graph the curves  y= x2- x  and  y =  x3 - 4x2 +3x  on acommon screen and observe that the region…

A: The given curves are as: y=x2-x   & y=x3-4x2+3x First of all we have to find the point of…

Q: Find the area under the curve 2x+3y-6%3D0 from x+63D0 to x-19%3D0

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Q: Calculate the area of the region that lies between the line y=-1 and the parabola y = x²-6x-1,

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Q: Find the area of the segment cut from the curve y=x (x-3) and the ordinates x=0 and x=5

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Q: Use a change of variables to find the area of the curved rectangle above the x-axis bounded by…

A: Given,Area bounded by:y24-1≤x≤4-y216 , y264-16≤x≤9-y236 , x≥0

Q: Find the area of the donut-shaped region bounded by the graphs of (x - 2)2 + (y + 3)2 = 25 and (x -…

A: It is given that the equation of two circles are x-22+y+32=25…

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.