the infinite region in the first quadrantbetween the curve y = e-x and the x-axis. Find the centroid of the region.

Q: Calculate the y-coordinate of the centroid of the shaded area.

A: Figure shows the cross section of the composite section: Divide the composite section into figure…

Q: Calculate the area of the shaded part y = x + 3 and y = x³ – 3x + 3. y3x+3 Area 1 Area 2 (2, 5) + y…

A:

Q: Find the centroid of the region cut from the first quadrant by the circle x2 + y2 = a2.

A:

Q: Find the centroid of the triangular region cut from the first quadrant by the line x + y = 3.

A: We will find the x and y-intercept of the triangle.  To find x-intercept we plug y=0 and find x…

Q: Determine the y-coordinate of the centroid of the shaded area shown. 13" Parabolic. 5" I 5" -x

A: We know that centroid coordinate y (y-)=∫05xf(x)dx∫05f(x)dx let equation of parabola is f(x)=…

Q: y = -a(x – h)? +k (-2.1 , 2.9) (1,n)

A: The given curve is y=-ax-h2+k. Here h=-1 and k=11 given. So the curves becomes y=-ax+12+11. Also the…

Q: dy dx √√₁² 2 = - X

A: Solution :-

Q: Determine the y-coordinate of the centroid of the shaded area. x = ky? I---x

A: The given problem is to find the y coordinate of the centroid of the given shaded region. Shaded…

Q: The region between the lines y=2x, y=x/3 and x=3.

A: Detailed solution of the problem is given below. Explanation:Step 1: Step 2:

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.