1. Find the area of the region bounded from the right by the curve x = 4 - y2 , from the left by the line y+x -2 and below by the x-axis.

Q: 1) Find the area of the region above the x axis and to the left of the line x = 1 bounded by the x…

A:

Q: Find the area of the region between the graphs of y = 20 - 2² and y=-2x - 15 over the interval 6 < x…

A: Please see the below picture for detailed solution.

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: 5. Find the area bounded by the curves y = x4 – 4x2 + 4 and y = x2. -2

A:

Q: 2. The area bounded by y=3x+4 and the curve y=x2 is revolved about the line x =5.

A: 2) The area bounded by the given curves is:

Q: 2. Find the area of the region enclosed by the parabola y = 2x² and the line y = -x-1

A:

Q: 2. Find the area bounded by the two curves y=x²-6x²+ 8x and y = x² - 4x.

A:

Q: 6. Find the area between the curve y = x(x - 3) and the ordinates x = 0 andx = 5.

A:

Q: 2. Find the area of the region bounded by the curve y = x^3 − 2x^2 − 5 x + 6, the x-axis, and the…

A: Given: y=x3-2x2-5x+6 For finding area of region bounded by given curve with x-axis and the lines…

Q: 1/ Find the area of the region enclosed between the curves y= 2x²+10 and y=4x+16 and ,x=-2 and x-5?…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 1. Find the area bounded between the curves: y = x+1, y = -2x + 7 and x = 0 A. With respect to the X…

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: 1) Find the area of the region above the x axis and to the left of the line x = 1 bounded by the x…

A:

Q: Find the area under the curve from x = 0 to x = 1 of y = (x 4 + x)5 (4x 3 + 1).

A:

Q: 1- Find the area of the region enclosed by the line y=4x and the curve y=x'+ 3x'.

A: According to our guidelines we can answer only first question and rest can be reposted.

Q: 2. Find the area bounded by the two curves y = x² - 6x²+ 8x and y = x² - 4x.

A: We have to compute the area between the given curves using the double integration method by first…

Q: 1. Find the area of the region between the curves y=x -4 and y=2-x.

A: As per our guidelines we are suppose to solve only first question if the multiple questions are…

Q: Find the area of the region bounded by the parabola y = 2x, the tangent line to this parabola at (4,…

A: Definition used -              Equation of a tangent line -                  (y-y1)=f'(x1)(x-x1)…

Q: 7. Find the area bounded by the curve y = 4x - x^2 and the lines x = 0 and y = 4.

A:

Q: 31. Find the area of the finite region bounded by the curves y = x(10 - x) and y = x (3x+ 2).

A: Q 31 Consider the curves, y=x10-x   and    y=x3x+2 To calculate the intersecting points between the…

Q: 1. Find the area between the curves x2-y = 9 and the line y 2x-6

A: Since you have posted multiple questions in this question which are not interlinked so I do only…

Q: 1. Find the area bounded between the curves: y = x°, x = 1, and y -8

A:

Q: 1. Find the area of the region bounded by the graphs of the equation y = x and y = x2.

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: 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: 8) find the area of the regions bounded by the curves: y=x' +x+2 and y = 2(x+1)

A: since you have asked multiple questions in single request so we will be answering only first…

Q: 14. Find the area of the region bounded by these two curves: X = y' – 2y and x-y-4=0

A:

Q: In(5z) – 1 to Find the area of the region lying between the r-axis and the curve y the right of the…

A: Using integration by parts,

Q: 1) Find the area of the region bounded by the curve y=3x•e-2* and the x-axis, for x>0. i) Rou imal

A:

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: 7. Find the area of the region under the curve y= |2x – 1| between x= O and x= 2.

A:

Q: 8. Find the area bounded by y = (11 – x)7, the lines 3x=2, x=10, and the x-axis.

A: We have to find volume of solid generated by revolution.

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

A:

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: 1- Find the area of the region enclosed by the line y=4x and the curve y= x³ + 3x².

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: ii, Find the area under the graph y=5x4 between the limits x= 1 and x-3.

A:

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: Find the area of the region lying between the x-axis and the curve y = In(7x) – 1 to the right of…

A: Consider the function y=ln7x-1x2. Find region between the curve to the right of line x=e and  x-axis…

Q: 6. Find the area of the region bounded by the two curves of equat rens a) x=3-y² and f(x)= 3x (スー2)-…

A: Note:- In Part (a), you mention f(x) for 2nd curve but it is not mentioned for first curve. If i…

Q: - 5. Find the area bounded by the curve y² − 3x + 3 = 0 and the line x = 4

A:

Q: 3. Find the area bounded by the curve y = x² - 7x + 6 and the x-axis and the ordinates x 2 and x =…

A:

Q: Find the area between the curves. y = x2 - 9x + 4 and y = x² + 6 from x = 0 to x = 6

A:

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

A:

Q: 1- Find the area of the region enclosed by the line y=4x and the curve y=x³ + 3x.

A: To. Find thhe area of enclosed region

Q: Find the area of the region between the curves y=x2-1 and y= - 2x² +2 from x= - 1 to x=1.

A:

Q: 1. Find the area of the region bounded by the graphs of the equation Y = x and y = x2.

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

Q: 3 2. Find the area bounded by the two curves y = x³- 6x² + 8x and y = x² - 4x.

A:

Q: 4. Find the area of the region bounded by the parabola x=y^2 +2 and the line y=x-8 *

A: Given curves are x=y2+2, y=x-8 We have to find the area bounded by this region.

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…

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.