Estimate the area under the graph of f(x) = 2x between x= 0 and x = 8 using each finite approximation below. a. A lower sum with two rectangles of equal width b. A lower sum with four rectangles of equal width c. An upper sum with two rectangles of equal width d. An upper sum with four rectangles of equal width

Q: Find the area under the graph of the function f (x) = xe-* between x 0 and x = 5.

A:

Q: Approximate the area under the graph of f(x) = x' over [1,3] by using N = 4 with left endpoints. 20…

A: The objective is to estimate the area under the graph of fx=x3 over the interval 1,3 by using N=4.…

Q: Use a finite approximation to estimate the area between the x-axis and the graph of f(x)=2x^5…

A:

Q: Find the area under the graph of f(x)= x2 and above the x-axis, between x = 0 and x = 3.

A: Given, f(x) = x2, we have to find the area under the graph f(x) and above x-axis between x = 0 and x…

Q: Calculate the area, in square units, bounded above by f(x)=x2+8x+16 and g(x)=8x+80 and bounded below…

A: The solution of the problem is given in the next steps.

Q: Determine the expression for the area under the curve f(x) on the closed interval [0, 3] with n…

A: Definition of the definite Integral

Q: Estimate the area under the graph 1 of f(x) = from a = 5 to x2 +1 b = 13 by using n = 4 rectangles…

A: The given function,   f(x)=11+x2 from a=5 to b=13 by using n=4 rectangles

Q: Find the area between the graph of function and the x-axis over the given interval, if possible.

A: fx=5x-22,  (-∞, 1].

Q: Find the total area between the graph of f(x)=x2−5 and the​ x-axis from x=0 to x=6.

A:

Q: Approximate the area under the graph of​ f(x) and above the​ x-axis using n rectangles. f(x)=x^2+2,…

A:

Q: (a) Estimate the area under the graph of f(x) = 25 – x from x = 0 to x = 5 using five approximating…

A: Consider the equation as shown below: Here, the function fx =25-x2 And the object is to find the…

Q: Find the area under the curve y = x3 + 3x2 and the x-axis between x = 1, and x = 3

A: Find the area under the curve y = x3 + 3x2 and the x-axis between x = 1, and x = 3.

Q: Find the area between the graph of f (x) = x² – 2x and the x-axis from x = -1 to x =

A:

Q: Estimate the area under f(x)=x^3 from x=1 to x=5 using n=4 rectangles and choosing heights via: (a)…

A:

Q: Approximate the area under the curve of y = x² - 2x + 3 over the interval x = -1 to x = 3 using 4…

A:

Q: Find the area between the curves f(x) = −x² + 4x and g(x) = x² - 6x + 8.

A: Basic identities of integration are used

Q: find the area between f(x)=x2 +16 and the x-axisn from x=0 to x=8

A: To determine the area between the curve and x-axis.

Q: O 1hr36mins X Estimate the area between the x-axis and the graph of f(x) = 9 – x² over the interval…

A:

Q: Let f(x)=-2x^ 3 +6x^ 2 -x+1, Use L 4 to estimate the area under the curve or the interval [- 1, 1]…

A: L4 is the left endpoint of the expression with 4 approximating rectangles.

Q: Find the total area bounded by the x-axis and the curve f(x) = x2 + 3x - 4 over the interval [0, 4]…

A: The given curve is,

Q: Consider the area under the graph of f (x)=x – 3x, from x = 2 to x= 4. a. Estimate the area under…

A:

Q: Find the area under the graph of f(x) = 3x2, above the x-axis, and between x = 0 and x = 2.

A:

Q: Find the total area between the curve of the function f(x)=−4x+8 and the x-axis over the interval…

A: To find the total area between the curve of the function f(x)=−4x+8 and the x-axis over the interval…

Q: The area of the region between the x-axis and the carve y = e¯ -3x for x >0 is

A: Formula:For y=fx; y≥0 area between the curve y=fx, x=a,x=b and x-axisA=∫ba fxdxGiven y=e-3x

Q: (a) Estimate the area under the graph of f(x) = 2 + 4x from x = -1 to x = 2 using three rectangles…

A:

Q: Given flx=e Estimate the area bounded between f(x) and the x-axis, over the interval -2sxs2, by…

A: Given Data The function is f(x)=e-x². The interval is -2≤x≤2. The number of rectangles is n=4.   The…

Q: Estimate the area under the graph of f(x) = between x =1 and x = 7 using the midpoint rule" with two…

A: According to the mid-point rule, we divide the interval into n sub-intervals and consider the height…

Q: Draw the graphs and find the area between the curves f (x) = x - x+3 and g(x) = -4x+1.

A: Let's find.

Q: Estimate the area under the graph of f(x)=5/x from x=1 to x=7. Approximate using 6 rectangles.A.) If…

A: There are 6 rectangles  So each rectangle is of width = (7-1)/6=6/6=1 So, endpoints are…

Q: Approximate the area under the graph of​ f(x) and above the​ x-axis with​ rectangles, using the…

A:

Q: a) Estimate the area under the graph of f(x)=2x+1 from x= 1 to x=2 using four approximating…

A: Given problems:- a).  Estimate the area  under the graph f(x) =2x+1 from x=1 to x=2 using four…

Q: Approximate the area under the graph of​ f(x) and above the​ x-axis using n rectangles. f(x)=6/x…

A: The width of the interval [2, 10] is = 10-2=8 There are 4 partitions. So the width of each…

Q: Find the approximate area under the function f(x)=2.5-2sin(πx/6) using the four middlescribed…

A: From the given picture we see that the middle points are x=1,3,5,7 So we find the x values at these…

Q: Find the area under the curve y=x3+3x2 and the x-axis between x=1 and x3D3. O 46 sq. units O 54 sq.…

A: We need to find the area under the curve y=x3+3x2 on interval 1, 3.

Q: Estimate the area under the graph of  f(x) = 4 + 4x2 from x = −1 to x = 2 using three rectangles and…

A: In this question, we find the area by using the midpoint rule for the given function f(x)=4+4x2 for…

Q: Approximate the area under the curve of f (x) = x² +3 from 0 to 4 using the Midpoint Rule with n =…

A:

Q: ii, Find the area under the graph y=5x4 between the limits x= 1 and x-3.

A:

Q: Find the area above the x-axis bounded by the function f(x) = -x2 + 2x + 3 and the x-axis.

A: Given that, f(x) = -x2 + 2x + 3 Points of intersection of f(x) with the x-axis are obtained when:…

Q: 7. Find the area bounded by the curve y = x e¯** , the x-axis and the maximum ordinate.

A:

Q: Find the total area between the function f(x)=3x+8 and the x-axis over the interval (−4,−1). Submit…

A: To calculate the unsigned (total area) of the region: in calculating total area, we take only the…

Q: Approximate the area under the graph of f(x) = 0.03x* - 1.44x + 43 over the interval [3,7] by…

A:

Q: Given the function f(x)=−x−2, find the total area between f(x) and the x-axis over the interval…

A: To find the area of the given region which may lie both above and below the x-axis.

Q: Find the total area between the curve of the function f(x)=−2x and the x-axis over the interval…

A:

Q: Approximate the area under the curve of y = x - 2x + 3 over the interval x=-1 to x = 3 using 4 right…

A: Find out the area under the curve using 4 right endpoint rectangles.

Q: Consider the function f (x) = x² + x + 2. What is the maximum approximation of the area under the…

A:

Q: Solve. 1. Find the area of the region between the function f(x) = 4x + 1 and the x– axis on the…

A: Note :As per our guidelines we are supposed to answer only one question if there are multiple…

Q: - Use the midpoint sum formula to calculate the area under the curve f(x) = x³ from x=0 to x-12…

A: Here h = b-an = 12-04 = 3

Q: Estimate the area between the x-axis and the graph of f(x) = 9 – x? over the interval [– 2, 1] by…

A:

Q: Estimate the area under the graph of f(x) = 1/1 + 4x^2 from x = −2 to x = 0 using four approximating…

A:

Q: Use the right endpoint sum to approximate the area under the curve f (x) = x^3 from x = 1 to x = 2…

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.