Find the area of the region bounded by y=x^2-6x+5, y=0 and the lines x=2 and x=5

Q: Plot the function f(y) =2y^2 − 2y and f(y)=12y^3-12y^2 and find the total areas of the shaded…

A: Graph of functions

Q: Determine the concavity of the graphs of y^2=x and y=x^3

A: We have to determine the convexity of the graphs of y2 = x and y = x3 in between the points of their…

Q: Find the area delimited by the functions f (x) = 9x ^ 3-13x-3; y g (x) = 8x ^ 3 + 3x-3

A: The graph is:

Q: Graph the function along with secant lines AP, BP, CP where A = (0, 9) B= (1,7) C = (1.5,4.5) P =…

A:

Q: Question 3.5: Calculate o dz. Question 3.6: Calculate o 1 - dz .

A:

Q: Find the area of the region bounded by f(x)=-x^2+6x-5, the x axis, and the lines x=2 and x=5. Graph…

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Q: Find the area intercepted by the three equations 4x^2-y^2+2x=1, y^2-x=4, and y=x-2 (Please answer…

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Q: Find the area between y = 6 - ² and y = x² 2 -5 -4 N 8+ 7 3 2 -1 -2 -3 The area between the curves…

A: The equation of curves are given y=6-x2 and y=x22-4

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

A:

Q: Find the areas enclosed by the following curves: (b) y = x4 – 4x² + 4_and y = x² y = x? 57 3- y = x*…

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Q: the shaded area shown in the figure is bounded by the line with equation y = 12-7x-x² and the line…

A: given functions are                                              y=12-7x-x2, y=4…

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.