Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle. 2x + y2 = 48, x = y %3D 20 15 15 10 10 -8 / -6 -4 2 4 6 -2 4 6 8 -6 -4 -5 -5 y y 8- 4 6. 2 -5 5 10 15 20 -5 10 15 20 -2 -8- Find the area of the region. 20

Q: Find the area of the region enclosed by the given curves. y = 2√√√√x, y = x - 3,x=0, x=4

A: Given y=2x, y=x-3 x=0, x=4To find area of region enclosed between two curves:

Q: Sketch the region enclosed by y=4x and y=3x^2. Decide whether to integrate with respect to x or y,…

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

Q: Find the area of the region in the first quadrant bounded above by y = -x2 + 6 and below by y = X. 8…

A: the solution is given below

Q: Find the area of the region in the first quadrant bounded by the curve y = √x² + 5, the x-axis and…

A: Given: y=x2+5 Graph of the functions given are

Q: Find the area of the region(s) enclosed by the curve y = |2x - 6|, the x-axis, and the lines x = 0…

A: Given: y=2x-6x=0 and x=4

Q: Find the area of the region in the first quadrant bounded by the curve y = √√x² + 5, the x-axis and…

A:

Q: Find the area of the region enclosed by the curves y=x+5, y^2=x, y=-1 and y=2

A: You need to draw the graph using the given details and find their intersection points. Then…

Q: Find the exact area of the region that lies under the curve given by y = 10/2x +1, 0<x <1 %3D

A: We know the area of the region that lies under the curve  y=f(x),  a≤x≤b is given by Area =∫aby dx…

Q: Calculate the area of the region bounded by the graphs of the given equations. x 2y2- 4, x = y2 + 5…

A:

Q: Find the area of the region bounded by the graphs of the equations.

A:

Q: Find the area of the region bounded by graphs of the two curves

A:

Q: FIND THE AREA OF THE REGION BOUNDED BY THE FOLLOWING CURVES: 1. y = x(x-3), x = 0, x = 5 2. y =…

A: Given

Q: Find the total area of the region enclosed by the curve x = y^(2/3) and the lines x = y and y = -1.

A: To determine the area bounded by the curves.

Q: Sketch the region enclosed by the given curves. y = 17xl, y = x2 - 8 y 40 4아 20 20 ma x -20 -40 50…

A:

Q: Find the area of the unbounded shaded region. 1 y = x2 + 1 y 1.0 0.5 .4 -2 2 05

A:

Q: Sketch the region bounded by the graphs of y =3y = 0,x = 4, and x= 7. Then compute the area. Area is…

A: Solution is given below:

Q: Find the area of the region enclosed by the line y=4 and the curves y=e^x and y=(x-1)^2

A:

Q: Determine the area of the region between the following curve. x = |y| and 2x = −y^2 + 2

A: Given that, x = |y| and 2x = −y2 + 2

Q: Find the total area of the region enclosed by the curve x=y^2/3 and the lines x=y and y=−1.

A:

Q: Find the area of the unbounded shaded region. y = ex/5 у 2.0 1.5 1.0

A:

Q: Sketch the region enclosed by the given curves and find the area.  y = 12 − x ² , y = x² − 6

A:

Q: Find the area of the region bounded by the given curves. y = √x,  y= -3√x.  y= x- 2

A: It is given,Function 1: y= -3x1  OR x1 = y29                        (1)Function 2: y= x2- 2   OR x2…

Q: Find the total area of the region between the curve and the x-axis. 2) y = (x + 1/x; 4 sx s 9

A:

Q: Compute the area of the shaded region. y=-x(x-2) 3 3/4 13

A:

Q: Sketch the region enclosed by the given curves. y = |2x|, y = x² - 3 y y 8 8 6 6 4 4 2 2 X -4 2 -4…

A: Let's find.

Q: Find the area of the region bounded by the given curves. c.)   y=4x-4x2, y=0, x=1, x=3     Ans.…

A:

Q: y=x2 -4x and y=2x -x2

A: y=x2-4x and y=2x-x2 Now, draw the graph of both the curve on the same coordinate system. From the…

Q: Sketch the region enclosed by the given curves and calculate its area. y= square root of x, y=0, x=4

A: Given,

Q: 6. Find the area of the region enclosed by the graphs of y = VT+1 and y = r – 2 and the vertical…

A:

Q: Determine the area of the given region. The region in the first quadrant bounded by y 4x and y =…

A: Equate y=4x and y=x25-x2 to obtain the interval of integration.…

Q: Find the area of the region in the first quadrant bounded by the curve y = √x² +5, the x-axis and…

A:

Q: Graph the equations and shade the area of the region between the curves y = x3 and y = x2 − 7x over…

A:

Q: Find the area of the given region y = tanh 2x

A: Given curve and figure: y = tanh 2x

Q: Find the area of the region in the first quadrant bounded by the curve y = √x² +5, the x-axis and…

A:

Q: 5. Calculate the area of the region enclosed by the graphs of y = 2r- r and y = 0.

A: We first find where they meet Plug y=0 in y=2x-x2 and solve for x

Q: Find the area of the region bounded by the graphs of the equations y = e, z = 0, z= 5, y = 0

A: To find the region bounded by the following graphs of equations,  y = ex  x = 0 x = 5 y = 0

Q: Sketch the region enclosed by the given curves. y = 13 – x2, y = x² – 5 y y 5 -6 -4 - 2 4 6 -6 -4 -2…

A:

Q: y =x.y = x, x> 0 1 1 y : X у —х, у — —х, х > 0 4

A: we need to use integration to find area between curves

Q: Find the area of the shaded region. y y= 5 x- x (3, 6) 4 2 y= 2 x X -1 1 2 3 4 5 CO

A:

Q: Find the area of the region cut from the first quadrant by the curve x^(1/2) + y^(1/2) = a^(1/2).

A: Sketch the graph x^(1/2) + y^(1/2) = a^(1/2) in first quadrant roughlyx goes from 0 to a y also goes…

Q: Sketch the region bounded by the graphs of the equations and find the area of the region y = x, y =…

A: We sketch the region using a graphing calculator

Q: Sketch the region enclosed by the given curves. y = x* - 15x?, y = x? 20 4 40 -6 -2 6 2 -20 20 -6 -4…

A:

Q: Graph the region bounded by the curves and determine the area of the region. x = y? – 2y; x = 0

A: ANSWER :

Q: Find the area of the region bounded by the given curves. y= x2, y = 4x - x2

A: The given curves are,   y= x2,  y = 4x - x2

Q: Sketch the region enclosed by the given curves and find the area. x = 2y ² ,  x = 4 + y

A: Sketch the region and integrate in y variable.

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

A:

Q: Find the area of the region bounded by the given curves. y = 2ax, y = 2ал*, а > 0

A:

Q: Consider the following equations. Y= (1)/ (x2 + 1), y=0, x= -1, x= 1 Sketch the region bounded by…

A: Here given curve is Y = 1/(x2 + 1) Y = 0 X = -1 X = 1

Q: Let R be the region enclose by the graphs of y=lnx, the line x=3, and the x-axis. Calculate the…

A:

Q: Find the area of the given region y = sech (x/2)

A:

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.