Find the area between the curve f(x) = −3x^2 + 3 and the x-axis over the interval [−1, 2].

Q: Find the area bounded by the curve y = x exp(-x²), the x-axis and the vertical line passing through…

A: Given: The given curve is, The x-axis and the vertical line passing through the maximum coordinate.…

Q: Find the area bounded by the curve y=4x-x² and the lines x=-2 and y=4.

A: See below

Q: Find the area under the curve f(x) = 2x* from x = - 3 to x = 2. Area %3D

A:

Q: Find the area bounded by the curve y = x2, AB is tangent to this curve at point P (2,4) and the x-…

A: Since you have asked a question with multiple parts in a single request we would be answering only…

Q: Find the area under the curve 4x²-3x+6 between x = -2 and x=3

A:

Q: Estimate the area under the graph of f(x) = 4 over the interval [2, 5] using five approxima %3D…

A: Given: f(x)=4x

Q: Find the area beneath the curve g(x) = 8x + 3x2 from x = 5 to x = 6

A: Given function is,

Q: Find the area between the curves x² and 3x – 2

A:

Q: the area bounded by the curves y=2-x2 and y=x2 is

A:

Q: Find the area bounded by the curve y = 4x over the square root of (1 - 2x) and lines y = 0, x = -4…

A:

Q: Solve the area bounded by the curve y=5-x^2 and the line y=2x. With graph.

A:

Q: d) Use the right endpoint rule to approximate the area under the curve of f(x) = 4- x2 on [1,2]…

A:

Q: Find the area of the region bounded by the curve f(x) = ex -3 and the x-axis , and between x = 0 and…

A: The region bounded by the curve f(x) = ex -3 and the x-axis , and between x = 0 and x = 2 is as…

Q: Find the area between the curve y = 4 – x² and the line y = -x + 2.

A:

Q: Determine the area bounded by the curves y = -x – 18x + 40 and y = (x - 2)2

A: The x coordinates for the points of intersection of the curves are given by:…

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: Find the area between the curves y = ln x and y = ln 2x from x = 1 to x = 5.

A: The given two curves are,

Q: The sum that best approximates the area under the curve between the function and x-axis on the…

A: our objective is to find the best approximation

Q: What is the total area between f(x)=2x−7 and the x-axis over the interval [0,5]?

A:

Q: Find the area bounded by the curve 2x2 + 4x + y – 0 and the line y + x = 0

A: To find the area of region bounded by the given curves.

Q: Find the area of the region bounded by the curve y = 9 - x2 and the x-axis.

A:

Q: Find the area bounded by the curve y (x- 2)(x + 1)(2x – 1) and x-axis.

A: We use integration to find the area.

Q: Find the area bounded by x2- 6x +y = 0, x² - 2x - y = 0. and the x-axis.

A: We have given two curves;

Q: Find the area between two curves f(x) = x² + 3x and g(x) = 6x.

A: The region bounded between the curves fx=x2+3x and gx=6x

Q: Approximate the area between f (x) = x² + 6x + 5 and the x -axis on the interval [0, 2] using 4…

A:

Q: Using left endpoints, approximate the area under the curve of f(x) =3x^(2) + 1 over the interval [0,…

A:

Q: FInd the area bounded by the give curves y=6x2-8x-2 and y= 3x2+4x-11

A:

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

A:

Q: 22) Find the area of the region between the curve y = 2x/(1 + x2) and the interval -2 sxs2 of the…

A:

Q: solve the area bounded by the curve y=4x-x^2 and the lines x=-2 and y=4

A: To find out the area bounded by the curves.

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 of the region bounded by f(x) = -x² – 2x + 3, x-axis, and interval [0, 2].

A:

Q: 2. Find the total area under the curve f(x) = 2xe² from x = 0 and x = 5.

A:

Q: Find the area between the curves: y=x^3-11x^2+18x and y = -x^3+11x^2-18x

A: y=x3-11x2+18x and y=-x3+11x2-18xTo find the area between the curves:

Q: Estimate the area under the curve of f (x) = x3 – 4x on [-1, 3] by calculating Lg and Rg. %3D

A:

Q: The area of the region bounded by x = /9-y', the y-axis and the line x-y in the first quadrant is:

A:

Q: Find the area between the curves: y=x^3−10x^2+21xx and y=−x^3+10x^2−21x

A:

Q: The area bounded by the curve y = 6x and the lines x = 7,x = 11 and x – axis ахis is

A: → y = mx is the equation of straight line passing through origin with slope m.→ Area of triangle =…

Q: Find the area between the curves x=63-7y^2 and x=7y^2-63

A: Here two curves are given and we need to find the area between them. The curve equations are shown…

Q: Find the area between x-axis and the curve defined by   y = 2·x2 − 6·x on the interval [0,4].

A: Given curve: y=2x2-6x We need to find the area between x-axis and the curve on the interval 0,4

Q: Find the area bounded by the curve 2y2+2y-x-2=0 and the line x= 2y

A:

Q: 6. Find the area bounded by the curves of y = 6x + x² andy = -x² - 2x, and the linex = 5.

A: The equation of the curves are  C1: y = 6x+x2C2: y = -x2-2xC3: x = 5 To evaluate: The area of the…

Q: 8) Find the area between the curves: y = x'-9x + 14x and y =-x +9x2 - 14x

A:

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 the curve y= 1--x² and the x-axis.

A: Given equation of the curve: y=1-19x2 To find: Area of the region bounded by the curve and x-axis.

Q: Estimate the area under the curve of f (x) = x3 – 4x on [-1, 3] by calculating Lg and Rg.

A: To find area under a curve y=f(x). Integrate f(x) from x = a to x = b.

Q: Find the area bounded by the curve y2 = 4x and the line 2x + y = 4.  Show full complete solution.

A: Given : Curve : y²= 4x              and line  2x+y=4 To find : Area between the curve and line

Q: Find the area bounded by the curves y=x4-2x2 and y=-x2+4 at an [-1, 1].

A: The region bounded by the curves y=x4-2x2, y=-x2+4 in [-1,1] is:

Q: Find the area bounded by the curve y=10+4x+x^2 and x-axis from x=-3 to x=-1.

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.