Calculate ∫∫(x^2 + y^2)^3 dA. Where D is the region in the first quadrant                  D                      bounded between the function y=x , y=√3x and the                                           circumference x^2+y^2=16

Q: Find the area of the region in the first quadrant bounded by the line y=2​x x=4​ y=2/x and the​…

A: The given region is bounded in first quadrant by following curve: y=2xx=4y=2x and the x-axis.…

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: Find the area of the “triangular” region bounded on the left by y = sqrt(x), on the right by y = 6 -…

A: It is given that,

Q: Calculate the total area of the region bounded by the line y= 6x^2 + 9, the x-axis and the line x =4…

A:

Q: Find the number b such that the line y = b divides the region bounded by the curves y = 16x2 and y =…

A: It is given that, y=16x2y=9   Area under the bounded region can be calculated by using,…

Q: Find the equation of the vertical line that divides the area of the region R bounded by 1 y = 20x2…

A: Identify the limits of integration from the given region, to calculate the area of the region. Here,…

Q: Find the area of the region bounded by the curves.  y = 8x2 and y = 1x

A: To find: The area of the region between the curve y=8x2 and y=x. Formula used: The area between the…

Q: What is the area (in square units) bounded by the curve y' =x and the line x- 4=0?

A:

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

A: Note: As you asked only part (b) so, I answered here only part (b).

Q: What is the area of the region between the lines y = 7x and y = 3x from x = 1 to x = 4?

A: 1.

Q: Find the area of the region between the line y = 2x and the curve y = x²+ x – 2

A: y=2x --------(1) y=x2+x-2 -------(2) For points of intersection…

Q: Find the area of the region in the first quadrant bounded on the left by the​ y-axis, below by the…

A:

Q: Find the area between the curves. x = 1, x = 2, y = 3x3 + 2, y = 0

A:

Q: Find the area of the region bounded by the curves y= 2² - 3 and y = 2x + 5.

A:

Q: Calculate the area of the segment cut from the curve y = x(3 – x) by the line y = x.

A: here we have to find the area of the region bounded by the curve and line.

Q: Find the area between the curves. x = 0, x = 6, y = 5x, y = 3x + 10

A: Given: The curves x=0, x=6, y=5x, and y=3x+10 . The bounded area between the given curves is shown…

Q: Find the area of the region in the first quadrant bounded by the line y=3​x, the line x=4​, the…

A:

Q: FIND THE AREA OF THE REGION IN THE FIRST QUADRANT THAT IS BOUNDED ABOVE BY y=sqrt(x) AND BELOW BY…

A:

Q: Find the area between the curves. x = -2, x = 1, y = 2x, y = x2 - 3

A: Given curves,  y = 2x y = x2 - 3 x = -2 x = 1 To find the area enclosed.

Q: What is the area of the region bounded by the y axis with lines?

A:

Q: What is the area of the region bounded between the curves y = 6x and y = 4x? What is the area of the…

A: 1) The given curves are  y=6x2 and y=4x First equate both curves 6x2=4x  6x=4    x=23

Q: Find the area enclosed between the curve y = 9 - x squared and line y = x + 7

A: This question is based on application of integration.

Q: Find the area of the propeller-shaped region enclosed by the curve x - y3 = 0 and the line x - y =…

A: x-y3=0  &  x-y=0⇒y3=x  &  y=x⇒y=x13  &  y=x Now the diagrammatic representation of the…

Q: Determine the area of the triangle bounded by the coordinate axes and the tangent to x² - y = 0 at x…

A:

Q: What is the area of the region enclosed by the curve y=x^2 and the lines y=x+6, x=0 and x=5?

A:

Q: Find the area of the region in the first quadrant bounded on the left by the y-axis, below by the…

A: The region bounded by the given curves in first quadrant. The curves can be used to find the limits…

Q: Use the midpoint rule with 4 rectangles to approximate the area of the region bounded above by y =…

A:

Q: find the area bounded by the given curves y=8x3+7 and y=8x+7

A: Given,           The curves are y=8x3+7 and y=8x+7.

Q: find the area of the region bounded by the curves 4x - y2 = 0 and y = 2x - 4

A:

Q: Determine the area bounded by the curve y = 2x - x^2 + 5 and the line joining the points (3,2) and…

A: Please see the explanation below

Q: Find the area between the curves. x = -2, x = 1, y = 2x2 + 5, y = 0

A: Given, x=-2,x=1,y=2x2+5,y=0

Q: Find the area of the region bounded by y = 4x + 9, y = -6x + 9 and x = 14. Leave your answer correct…

A: Area of region bounded by given curves are evaluated.

Q: Find the area between the curves. y = x4/3, y = 2x1/3

A: y = x4/3, y = 2x1/3

Q: Calculate the area between the curves y = 7- 2x2, y = x2 + 4, and the x-axis.

A:

Q: the

A: Given curve y^=x and y=√x  Line x-4=0   Find area ?

Q: estimate the area under the curve y=x^1/2, from x=1 to x=3 using right end point estimate

A: SolutionGiventhe curve y=x,from x=1tox=3 we need to estimate the area  under the curve y=x1/2,from…

Q: Find the area on the first quadrant bounded by the curve y = 2Vx and the lines y = 1,x = 4 and the…

A:

Q: Find the area of the region between the curves 4x + y = 12 and x = y. Area between curves

A: Solution

Q: find the area between the two curvesx=2-y^2x=y^4

A: Given thatx = 2-y2         ...(1)x = y4            ...(2)

Q: find the region bounded by the curves  y = sqrt(x) y=2-x x = 0

A:

Q: Calculate the area described by the equation y= -6x² +24x + 10, bounded by the lines x = 0 and x =…

A:

Q: Find the area of the region bounded by the curves y = x 2 − 3x + 5 and y = 3x + 5.

A:

Q: Find the area between the curves y = 4x – 3 and y = x². %3D

A: Given data is : y=4x-3     .....1 y=x2      .....2 From equation (1) and (2) ,…

Q: y = 2x 2 − 8x + 12 and y = −2x + 12.

A:

Q: Find the area of the region bounded by the three curves y = x², y = 8 - x², and 4x - y + 12 = 0.

A: Given: y=x2y=8−x24x−y+12=0

Q: Find the area of the region between the curves 4x + y = 12 and x = y. Area between curves =

A: R

Q: Find the area bounded by the curve 4y² + 16x – 15 = 0 and the linex = -1. %3D

A:

Q: Find the area of the region bounded by y = 7x + 7, y = -9x + 4 and x = 15. Leave your answer correct…

A: The solution of the problem is given in the next steps.

Q: Find the area bounded by the curves, 2x² + 4x + y =0 and y = 2x.

A:

Q: Find the area of the region in the first quadrant bounded by the line y = 8x, the line x = 1, the…

A: Intersection Points are:  The line x=1 will intersect the x-axis at (1,0) because y is 0 at…

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.