Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle. y = 2 + x3,   y = 5 − x,   x = −1,   x = 0   Find the area of the region

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: 3 Shade the area of the region bounded by, x² + y? p Hence, find the area of the specified region…

A: Giv

Q: Find the area of the region enclosed by the graphs of the given equations by partitioning the…

A:

Q: Shade the area of the region bounded by, x² + y? p Hence, find the area of the specified region…

A: we use integration to find area between curves

Q: Find the area of the region. 5ex y = 1 + e2x y 4 3 x = In V3 2 1 -2 -1 2)

A:

Q: 3. Find the area of the region in the first quadrant that is bounded by y=Vx , x-axis and y=x-2. |

A: 3) To find the area under the curve in first Quadrant

Q: In the given question , sketch the region bounded by the graphs ofthe equations and find the area of…

A:

Q: 4. Find the area of the shaded region by integrating with respect to 'y', y-2x-4 1.-2)

A: The area between two curves f1 and f2 between the points y=a to y =b is given by; A=∫ab(f2-f1)dy

Q: Sketch and shade the region y = x² – 1, hence find the total area between the given curve and the…

A: The standard form of a parabolic function is where (h, k) is the vertex. This standard form is also…

Q: Consider the following. y = x2 y = 12 - x 16 14 12 101 8- 6- 8 10 12 (a) Find the area of the region…

A:

Q: 6.(. Find the area of the region enclosed by the curves y = x² +1 and y = x +3.

A: I am solving this in step 2

Q: Find the area of the region between y² = x and x = y +2.

A: Given,  y2 = x   and  x = y+2  We have to find the area of region between y2 = x   and  x = y+2

Q: Find the area of the region enclosed by the graphs of 1 0, and x = 10 1 y = 0, x 1 — 25л2 NOTE:…

A:

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

A:

Q: SOLVE STEP BY STEP Sketch the region bounded by the curves y = vx + 4 , y=x+2 and evaluate the area.

A: the given curves are: y=x+4 and y=x+2. we have to skecth the region bounded by the given curves and…

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: Determine the area of the region bounded by y = xvx2 + 1, y = 1 e 2x, x = -3 and the y-axis. %D

A:

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: Consider the following. y = x2 y 20 - x 25 20 15- 10- 5- -10 -5 10 15 20 (a) Find the area of the…

A: Topic = Application of integration

Q: Find the area enclosed by the given curves. 20) y = 2x - x2, y = 2x - 4 %3D

A: We first sketch the region using a graphing calculator

Q: Sketch the region bounded by the graphs of the given equations and find the area of that region.…

A: Area between curves

Q: Find the area of the region bounded by the graphs of the given equations by partitioning the y-axis.…

A: Given equations: y=lnxx=ey=0 Its graph:

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 enclosed by the graphs of the given equations by partitioning the…

A: Given: y=x, y=x3, about x-axis

Q: The area formed by the boundaries y=1, x=2, and y=e^(-x) is closest to:

A:

Q: Find the area of the region bounded by y = 4(x + 2), x = 2 and the x-axis. Answer:

A: Given query is to find the area bounded by the curves.

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: 4.Find the area of the region bounded by the curves y = x² – 2x and y = x.

A:

Q: Find the area of the region enclosed by the graphs of 1 y = 1 y = 0, x = 0, and x = V1 – 16x2 NOTE:…

A:

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: 3. Find the area of the region enclosed by the given curves. y = Vx + 2, 1 y = x = 0, x = 2 %3| x…

A: Recall: If f(x) and g(x) are two continuous function and f(x) ≥g(x) on the closed interval [a,b] ,…

Q: Find the area of the region under the given curve from 1 to 5. x2 + 8 y = 6x – x2

A: The area under a curve is the area between a curve f(x) and the x-axis on an interval [a, b] is…

Q: Find the area of the region bounded by the graphs of y = 2e−x , y = 0, x = 0, and x = 2.

A: Given equations: y=2e-xy=0x=0x=2 The region bounded by the graphs of these equations is shown below:…

Q: 5. Find the area of the region bounded by y = e", y = e¬¤ and x = 2

A: We have to find the area of the region

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: Find the area of the region enclosed by the given curves. y = 13-x2, y=x2-5

A:

Q: y² = x y = x³

A:

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: Determine the area of the region between the x-axis and the graph of the curv -1 from x- 0 to x- 4.…

A: Area bounded by curves :   If f(x) and g(x) are two continuous function on a,b and f(x)≥g(x) on a,b…

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

A:

Q: 8. Sketch the curves and determine the area of the region formed in the given interval: y = √√2x, y…

A:

Q: Sketch the region below the curve y = x – x² and above the x-axis and find its area.

A:

Q: etch the region enclosed by y = x²y = √√x,x = 0,x = 1 and find its area.

A:

Q: Find the area of the region between y2=x and x=y+2

A: The area between curves is the area between a curve fx and a curve gx on an interval a, b given by…

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

A: The diagrammatic representation of the area is,

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

A: The equation of curves are : y=4x and y=2x2

Q: Find the area of the region bounded above by y = x + 6, bounded below by y = x², and bounded on the…

A: We need to calculate the intersection points of the given curves. So,…

Q: 2. Find the area of the region between the curve, x = y² + y −6, y- axis and y=0; y = 3.

A: we need to find the area bounded by the given curves.

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.