4. Find the approximate value of the area of the region bounded by the x-axis, the graph of f(x) = x² +x+1. over the interval [-1, 1] using four equal subintervals. a) Left-hand sum b) Right-hand sum

Q: Estimate the area under the line y= 2x+1 using six rectangles and right endponits over the interval…

A:

Q: Find the area of the region bounded by the graph of the following functions y=x2, y=-x2 +3

A: The given functions are:To find: The area bounded by the given functions.Concept:The area between…

Q: Q1) Estimate the area under the graph of f(x) = x² + 1 from x=1 to x=3 using four approximating…

A:

Q: Consider the image attached of the graphs of y = (1/2)x + 5 (what the red line represents) and y =…

A: Given y=12x+5  and y=x

Q: Estimate the area under the graph of f(x)=1/x+3 over the interval [-1,2] using ten approximating…

A:

Q: 3) Use approximating rectangles to approximate the area under the curve y = 4 – x2 on the interval…

A:

Q: Estimate the area under the graph (sqr-root):x+4 over the interval [-4,12] using 8 approxiamating…

A: Given function: Width of each interval = (12-(-4))/8= 16/8= 2  So the partition is -4, -2, 0, 2, 4,…

Q: 1* quadrant area of y = (4-x)/(x+2)²

A: Given  Curve y=(4-x)/(x+2)2  To find  area bounded by curves in first quadrant

Q: Find the area of the region between the graph of y=11-x2 and y=4x-49 over the interval where is is…

A: The given problem is to find the area of region between the given graphs y=11-x2 and y=4x-49 over…

Q: Find the area under the graph of y = 2x² - 2x + 4 on the interval [-2,0].

A: y=2x2−2x+4 on the interval [−2,0]

Q: Approximate the area bounded by the graph of Ax) = -x² + 9, the x-axis, and the vertical lines and…

A:

Q: Graph the function in the given interval. Then find the total area of the region between the curve…

A:

Q: Use rectangles to estimate the area under the graph of ƒ(x) = 4 − x², above the x-axis and from x =…

A:

Q: a) Graph the region bounded by y = x2 - 1. y = 1- x indicate and label a representative b) Find the…

A: It is given that, the function y=x2-1 and y=1-xWe have to find: (a) Graph the region bounded by…

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.