etermine the area bounded by the curves f(x) = x² – 16x + 24 and g(x) = –8x + 12

Q: Sy 5x – 10 Find the region with points that satisfy both inequalities.

A: y≤-x+2y>5x-10

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: 1. Find the area of the region bounded from the right by the curve x = 4 – y? , from the left by the…

A:

Q: Find area of region f(x)=x2-10x+9 g(x)= -x2+8x+9

A:

Q: 3 3 2 Find the area bounded by the curve y=x²-x² + 3x and the line y=x. 16 4 10 square units 8…

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Q: * Example (6): Find the area between the curve x = y² and the line x = y + 2 Solution :

A:

Q: Graph the curve Y = - 2 x (x - 4)(x + 6)(x - 2) between the value of x [0, 4], then find the area of…

A:

Q: Suppose we want to know the area of a region that is bounded by the graph of F(X)=1/2x+2 and the…

A: Consider the given curves.

Q: Find the area bounded by the parabolas (x - 1)² = 4ay and y² + 4a = 4ax.

A:

Q: 5. Find the area between the curve y, =x² - 4x +12 and y, = x² from 0<x<4

A: Given curves are y1=x2-4x+12y2=x2 Also 0≤x≤4

Q: Find the area between the curves f(x) = −x² + 4x and g(x) = x² - 6x + 8.

A: Basic identities of integration are used

Q: Find area of region f(x)=x2+4x+4 g(x)=4x+13

A:

Q: Find the area of the region bounded by the graph of g(x) = (x − 4)^4 and the x-axis between x = 2…

A: From the given curves

Q: Find the area between the curve y = x² + 7x + 12 and the x-axis from x = -3 to x = -1. Step 1 Notice…

A:

Q: 1. Find the total area bounded by the curves y=x²-3x and y = x³ + x² −12x.

A: Given Graphs y=x2-3xy=x3+x2-12x First we find point of intersection of graphs…

Q: find the total area between the curve g(x)=x^3 + 2x^2 -x-2 and the x-axis, from x=0 to x=2

A:

Q: The area of the region between the x-axis and the carve y = e¯ -3x for x >0 is

A: Formula:For y=fx; y≥0 area between the curve y=fx, x=a,x=b and x-axisA=∫ba fxdxGiven y=e-3x

Q: 1 Find the area bounded by the curve y=- =-=-—-—-x³-3³² x ² + 16 4 -x2 + 3x and the line y=x.

A:

Q: Find the area between the curve y = x² + 12x + 27 and the x-axis from x = -3 to x = -1.

A:

Q: What is the area of br^2 of the region bounded by

A: The given question is taken from the calculus in which we have to find the area bounded by the given…

Q: 1) Determine the area of the largest possible rectangle whose base is on the x-axis and the top two…

A: Given the rectangle whose base is lies on x axis and the top two corners lie on the curve y=9-x2

Q: 1. Find the area of the region bounded by the given curves. a) y = 2x° - x² - 5x + 4, y= - x² +3x…

A: We have to find the bounded area by curves

Q: The area bounded by the curve y = 14.x and the lines x = 4 and x = 6 above the x- axis is 364 square…

A: Area=∫ab(upper curve-lower curve)dx∫xndx=xn+1n+1+C

Q: Example 3.10: Find the area of the region between the x-axis and the granh of f(x) = x – x –- 2x,-1<…

A: We have to find the area of the region between the x-axis and the graph of fx=x3-x2-2x, -1≤x≤2.

Q: - Determine the area bounded by the curves y = -1² – 16x + 80 and y = (x – 4)°.

A:

Q: 1. The area bounded by the curves y x2,y 0, x = 2,x = 5 is 39. 2 is 10

A:

Q: 5. Find each of the two areas bounded by the curve y = x3 – 4x and y = x² + 2x. Solve in two ways.

A: Consider the two curves: y=x3−4x and y=x2+2x. The area of the region bounded in interval x∈a,b by…

Q: 1. Determine the area of f (x) = 3 + 2x – x² and above the x axis. - X - 3x 3 3 2. Determine the…

A: To find the area of f(x) and above the x-axis, use the formula, A=∫-13f(x)dx and substitute f(x)…

Q: Find the area of the region enclosed by the curves f(x) = 7x + 1 and g(x) = 5x + 17, and the lines x…

A:

Q: Using a graph, it can be shown that the roots of the equation x V4 – x² = 2 – x are x x 0.81 and x =…

A: Given curves, y=x24-x2,y=2-x and roots of the equation x24-x2=2-x are x=0.81,x=2

Q: 1. Find the area bounded by the curves y = 3x'+1 x=0 y= 3x+1 x-1 А. 3/2 5 В. 3/4 2 С. 1/4 -2 -1/0 21…

A: y = 3x3+1 , y = 3x + 1

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

A:

Q: Problem - 21: Determine the area bounded by the curves y = –x2 - x2 20x + 69 and y = (x – 3)². - - -

A:

Q: 1 3 Find the area bounded by the curve y== -x3. -x² + 3x and the line y=x. 16 10 square units 8…

A:

Q: 1. find the exact area of the region that lies beneath the curve y = 6x-4 , 1 </= x </= 6. 2. Find…

A: y = 6x-4given interval 1≤x≤6 Area of the region =∫abupper function - lower function dx we need to…

Q: Q1: The area of the region bounded by the graph of y=-0.5x+4and y=3x in first quarter.

A:

Q: 11. Find the area bounded by the curve y² + 2x - 2y - 3 = 0 and the y-axis.

A:

Q: Find the area of the region between two curves f(x) = 3x + 1 and g(x) = x from x = 0 to x = 1.

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: The area of the region bounded by the 2 curves f(x) = x² + 1 and g(x) = 2x + 1 is best described by:…

A:

Q: 1.5: The area of the region enclosed by the graph of f(x) = -√x and the x- axis on the interval [0,…

A:

Q: 5. Find the area of the region that is enclosed by the graphs of the functions: y=-x? - 3x + 4 and…

A:

Q: 1. Find the area between y = - x² + 4x and y = x² - 6x + 5. Graph and shade the area required.

A:

Q: 18: Find the total area of the region between the functior F(x) = x3 – 4x² + 3x and x-axis from…

A: The given curve is we have to find the area bounded by the region f(x)  and x-axis from [-3,3].

Q: The area of the region bounded by the curves f(x)=x²+1 and g(x)=2x+1 is best described by: a. ² [(2x…

A:

Q: 19. (a) Find the area bounded by the curves y = 2x2 and y = 4x. (b) Two cars both start on a journey…

A: Given two functions: y=2x2 and y=4x To find a) Area under the two curves b) If two curves represent…

Q: Consider the graph of y 2Vx between x 0 to x 9 and the graph of the vertical line x= 9 as shown…

A: Given that:

Q: Find the area of the region bounded by the curve y = x³ – 2x² – x + 2 and the x-axis for -1 <x<2, as…

A: We will solve this question by using double integration. where,  y=0 and y=x3-2x2-x+2 and x lies…

Q: Find the area between the curves f(x) = x^2 - 4x +12 and g(x) = x^2 - 2x + 2  for 0 ≤ x ≤ 3

A:

Q: Find the area of the region bounded by the graphs of the algebraic functions. f(x)=x^2-14x g(x)=0

A: SOLUTION-

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.