1/ Find the area of the region enclosed between the curves y= 2x2+10 and y=4x+16 and ,x=-2 and x=5? ans/ 142/3

Q: 2/ determine the area of the region enclosed between the curves x= 0.sy-3 and y=x-1? ans/ 18

A: Topic- Application of Integration

Q: Explain how to compute the area between the curve y=x^3-x^2-3x+3 and the x-axis from the values x=-2…

A: Let's draw the curves : Red shows curve of x3-x2-3x+3 .Blue shows curve of x =-2 .Green shows curve…

Q: find the area of the region bounded by the curves y=x3 and y = x² between their intersections.

A:

Q: Find area between the curves y=17/(9+x^2) and y=13/(1+x^2)

A:

Q: Find the area of the region between the curves 4x + y^2 = 12 and x =y.

A: 4x+y2=12    and  x=y

Q: Find the area under the curve y = 3xe for æ > 3. area =

A: Given:The given curve is y=3xe-x and x≥3To find:we have to find the area under the curve

Q: Find the area under the graph of y = (x + 1)^-2for x ≥ 0.

A:

Q: Find the area bounded by y = x^2 -1, and the line y = 3. * 31/3 sq. units 35/3 sq. units O 37/3 sq.…

A:

Q: Solve the area bounded by the curve x=y^2 and the line y=x+1, y=2, and y=-2. Graph manually.

A:

Q: Find the area under the curve y = x^2 on [3, 10]. a. Use four rectangles. b. Find the exact area.

A: a)-We have   fx= x2We want to calculate over the interval 3, 10 with 4 rectangles, thus…

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.