f(x) = 4x1/3 + x4/3 Find the area of the region bounded by the graph of the function f and the lines  y = 0, x = −1 and x = 1.

Q: Sketch the region bounded by the graphs of the equations f(x) = − 4/x3,         y = 0, x = −3, x =…

A: The graphical representation of the region bounded by the above equations is,

Q: Find the area bounded by the curve y = - -x³x²+3x and the line y=x. 16 4 (A) 10 square units B 8…

A:

Q: We must integrate y = (8x-x2)-(2x) = 6x-x². The limits on the integral correspond to the smallest…

A:

Q: What is the area of the region between the graphs f (x) = 3x – x and x – axis from x = 0 and x = 2 2

A:

Q: Q2/ Find the area of a region bounded by the curve f(x) = 8x' and x-axis and the two lines x=1, x=3.…

A:

Q: Shade the area of the region bounded by, x² + y2 < 7² and |x| + |y| 2 7 Hence, find the area of the…

A:

Q: Consider the region bounded above by f(x)=−x2+9x+7 and below by g(x)=8x+5. Find the area, in square…

A:

Q: Find the area of the region bounded by the graphs of the equations: f (x) = V5x – 10 g(x) = 2x – 4

A:

Q: 16. Find the area of the region bounded by the graphs of the equations, y = -x² +x+ 6, y = 0

A:

Q: Sketch the region bounded by the graphs of the equations f(x) = x2 + 2x, g(x) = x + 2 and find the…

A: The region bounded by the graph is as below

Q: The total area bounded by the graph of y = r- 1 and the x-axis is represented by 2.

A:

Q: Find the area of the region in the first quadrant bounded by the curve (x + 2)² y = 4 – x. [Use the…

A: Given that: (x+2)2y=4-x

Q: Consider the region bounded by g(x)=7x−6 and f(x)=x2+19x+14. Find the area, in square units, between…

A: The given two curves that bounds a region is,

Q: 2. Find the area of: (a) the region bounded by y = x^2, the x-axis and the line x = 2 (b) the region…

A:

Q: region

A:

Q: 2. Determine the area of the region bounded by the curve y = x³ – x2 – 2x, and а. the x-axis b. the…

A:

Q: Find the area between two curves f(x) = x² + 3x and g(x) = 6x.

A: The region bounded between the curves fx=x2+3x and gx=6x

Q: b) Find the area between the 2 curves f(x)=x²+4-4x and x-axes and border with the two lines = 5 &x=…

A:

Q: Find the area of the region between the graphs of the equations = x and y = 2 – x.

A:

Q: Sketch the region bounded by the graphs of the equations f(x) = 3√x − 1,   g(x) = x − 1 and find the…

A:

Q: The area of the region between the curve y x'-6x+ 8 and the x-axis & x=0; x= 3 is given by -6x+8)kke…

A:

Q: Find the area of the “triangular” region in the first quadrant that is bounded above by the curve y…

A: Consider the provided curve,  Bounded above by the curve y=ex2 and below by the curve y=e-x2. And on…

Q: What is the area of the region bounded by the curves y=f(x)=x3-4x2+5x and y=g(x)=3x-x2 between x=0…

A:

Q: Find the area bounded by the curve x = y² + 2y and the line  x = 3.

A:

Q: 2 Find the area of a triangle bounded by the y axis, the line f(x) = 8 – -x, and the line…

A:

Q: f (x) = x – 2x – 3

A:

Q: The region is bounded by the curve y = 6x – x² and y = x² – 2x –

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Find the area of the region completely enclosed by the graphs of the functions: y = x – 2, y=square…

A:

Q: Example: Find the area of the region in the first quadrant that is bounded above by Y1 =Vx and below…

A: The graph is shown below:

Q: Find the area of the region bounded by the  graph y=2x2-3x+2 the x axis and the vertical lines x=0…

A:

Q: of the given equations. y = x² - 2x - 24, y = -x² 1

A: Given curves are      y=-x2             . . . (1)    y=x2-2x-24  . . . (2) The graph is given be

Q: Find the area of the region bounded by the curve y^2 = 4x and the lines x = 1 and x = 4.

A:

Q: Find the area of the region above the x-axis bounded by the function y = 4x - x2 – 3

A:

Q: Find the area of the region between the graphs of y = 13 – x² and y = over the interval 3 < x < 8. –…

A: Solve by integration

Q: Find the area of the region bounded by f(x)=X^2-4X +3 the X axis in the lines X=2 and x=6

A: We will find out the area of the region.

Q: Solve the area bounded by the curve y = 4x-x and the lines x=-2 and y = 4. 12) Sketch of the curves:…

A: The given problem is solved below in detail.

Q: 2. Find the area of: (a) the region bounded by y = x^2, the x-axis and the line x = 2 (b) the region…

A:

Q: Find a such that the line x = a divides the region bounded by the graphs of the equations into two…

A: Given, y2=4-xx=0

Q: Find the area of the region bounded by the graph of the function y = the x-axis, and the lines x = 4…

A: Definition used-                 The area under the curve of a function f(x) is given by -…

Q: The area of the region bounded by the function f(x) = + 3, lines x = −2, x = 2 and the x — axis is…

A:

Q: Find the area of the region bounded by the curves: y=x^2+2x  and y=-x+4

A:

Q: Find the area of the region that is completely bounded by the two curves f(x) equals -X^2-3X +20 and…

A: We have to solve

Q: The area of the region bounded by x = /9- y2, the y-axi first quadrant is:

A: Here we have to find the area bounded by the region x=9-y2 .....................(1), the y-axis, and…

Q: Find the area (sq. units) covered by the line y = -Gx+ 3) from x1 = -8 to x2 = 0.

A:

Q: Find the area of a triangle bounded by the yy-axis, the line f(x)=10−2xf(x)=10−2x, and the line…

A: Now, from the graph we have the points of intersection of the lines

Q: Find the area bounded by the curve f(x) = x³ + 3x² – 4x – 5 and x-axis from x = -3 to x = -1 using:…

A: Consider the given area bounded by the curves as y=x3+3x2-4x-5 and the x axis from x=-3 to x=-1. Let…

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.