You must show tlhe detailed steps for all questions. No credit will be given if you do not show your work (a) Use the Itnit process to find the area of the region bounded by the graph of the function and the r-axis over the given interval; (b) use the fundamental theorem of caleulus to verify your result; (c) find the average value of the function over the given interval 2. f(z) 2r3 +2 +3, [0,3

Q: To find the average value of a function g(x) over the interval [a,b] you need to: Take the limit of…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: show steps please.

A:

Q: Use the Midpoint Rule with n = 4 to approximate the area of the region bounded by the graph of the…

A: The function is given as fx=cos x The interval is given as 0, π2

Q: For the integral dr Vx+4 (a) Find the average value of f on [0, 5]. (b) Find a number z that…

A: Given: - The integral is, ∫051x+4dx (a) To find: - The average value of f on 0,5

Q: Consider the function f(x) = 4x2 −x3. Provide the graph of the region bounded by f(x) and the x-axis…

A: The solution is given below in the next step:

Q: 1. Find the area of the region bounded from the right by the curve x = 4 – y? , from the left by the…

A:

Q: 5. (a) If f(x) = x · 2*, give an estimate of the net area of the region bounded by fand the x-axis…

A:

Q: Approximate the area bounded by the curve of the function f(x)=1/x , x axis, and the interval [1,3]…

A:

Q: Find the approximate area under the curve of y = 4x by dividing the interval between x= 3 and x 5…

A:

Q: 1.) Approximate the area under the curve y=f(x) between x=0 and x=10 using the Trapezoidal Rule with…

A:

Q: 4. Consider the functions f(x)= ax' and g(x)= ax, where a>0 is a real number; let R be the region in…

A: We roughly sketch f(x)=ax3 and g(x)=ax The shaded region will rotate about the x-axis. We find…

Q: Use the Midpoint Rule withn = 5 to approximate the area of the region bounded by the graph of f and…

A:

Q: 6. Use the Method of Midpoint Rectangles (do NOT use the integral or antiderivative) to approximate…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Find the area of the region bounded by f (x) 3D а у 20— Зх — 2х2 and the x -axis using Simpson's…

A:

Q: Find the survace area of revolution about the x-axis of y= 4sin(2x) over the interval x is greater…

A: Given: The curve y=4sin2x for 0≤x≤π2 To find: Surface area of revolution of given curve about…

Q: 2. Find the area of the region R enclosed by the curves given by the graphs of f(x) = v3x, g(x): =…

A: Area between curves

Q: 28 Find the area of the region bounded by the curve y = (x-1)' and the x-axis from x=0 to x= 2.

A:

Q: a)i) Calculate the area of the region enclosed by y=x2 , lines x=1 , x=3 , and the x− axis. Round up…

A: The Given curve is y = x2 The equation of the parabola is  y = x2. The vertex is at (0 , 0 ) and the…

Q: Consider the function f (x) = 5 cos x. What is the estimate of the area under the curve of f using…

A: Given that the function f(x)= 5 cosx . Here we have to estimate the area under the curve of f using…

Q: Q1: Use the horizontal and vertical cross sections to find the limits of integration for the region…

A:

Q: A CAT scan produces equally spaced cross-sectional views of human organ. Suppose a CAT scan of a…

A: Here we have to calculate the volume of liver which is area times thickness

Q: Consider the functions f(x) = ax and g(x)= ax, where a >0 is a real number; let R be the region in…

A: given functions are                                              f(x)=ax3, g(x)=ax, a>0 only in…

Q: Given the function f (x) = a) Find the average value over the interval [1, 4]. b) Find the value c…

A:

Q: Calculate the area of the region enclosed by y = x2 , lines x =1, x = 3, and the x − axis. Round up…

A:

Q: Using the left-hand endpoint with n = 8to write the Riemann Sum that describes the estimation of the…

A: Given: f(x)=x2+1 n=8 [a,b]=[0,2]

Q: Find the area of the region bounded by the graph of f(x) = Jx, the y-axis, and the tangent line to…

A:

Q: The radius and height of a right cylinder are measured at 2.9m and 1.6m respectively with a maximum…

A:

Q: = Find the area A of the region that is bounded between the curve f(x) = ln (x) + 1 and the line…

A:

Q: Using the right-hand endpoint with n = 8 to write the Riemann Sum that describes the estimation of…

A:

Q: Q3) Find the average value of the function f(x)=√cos 4x+1, on [0,1 Q4) Using Numerical Integration…

A:

Q: Find the area of the region that is bounded above by the curve f(x) = (x + 2)² and the line g(x) = 4…

A: NOTE: Refresh your page if you can't see any equations. . here we have first, we need to find the…

Q: Find the average value of the function over the given interval. y= x^2-2x+3; [0,7] show all work

A:

Q: Find the average value of a function over an iterval Quëstion Determine the average value of g(x) =…

A: Given function

Q: Use the Midpoint Rule with n = 4 to approximate the area of the region bounded by the graph of f and…

A:

Q: 7. Find the area bounded by the curve y = x exp(-x²), the x-axis and the vertical line p through the…

A:

Q: To find the average value of a function g(x) over the interval [a,b] you need to: Take the limit of…

A: Average of the function f(x) is given by : Avg. = 1T∫0tf(x)dx

Q: a) For f(x) = 2x + 1, 0sxS 3, estimate the area between the line and the x-axis with a Riemann sum…

A: solution is given below..

Q: We have used little vertically oriented rectangles to compute areas. There is no reason why little…

A: according to our guidelines we can answer only three subparts and rest can be reposted.

Q: Consider the Surge funchon f(x)= 6xe* a) compute the indefinite integral (f(x) dx. b) Find the…

A: Given: fx=6xe-x To Find: a To compute the indefinite integral, ∫fx dx.b To find the average value of…

Q: For the area under the curve f(x) = x(x+1)(x-7) above the x-axis, and between the vertical lines…

A:

Q: Q1/ Find the area of the region bounded by the given curve (y = x² - 5) and the curve (x = -) by…

A:

Q: Consider the function f (x) = 5 cos x. What is the estimate of the area under the curve of f using…

A: (Solving the first question as per our guidelines) Solution: We have to estimate the area of the…

Q: The area of the shaded region under a graph of a function y=f(x) equals 14 square units. What is the…

A: The area of the shaded region is given as 14 square units The given interval of shaded region is…

Q: Use the left-endpoint approximation to approximate the area under the curve of f(x) 3 on the…

A:

Q: Find the area under the curve f(x) = x° on x =[- 2.5, 5.5] using the Midpoint Rule with n = 8

A:

Q: 1. Find the area bounded by the curves between the curve y=1+x and the line y-1 x

A: area between curve

Q: Find the average value of f(x) = 4-x2 on the interval [2,3] Find the area enclosed by f(x) = -x2+4x…

A:

Q: Q.1. Use (i). Midpoint rule (ii). Trapezoid Rule and (ii) Simpson's Rule with n = 6 to find the area…

A:

Q: Using the right-hand endpoint with n = 8 to write the Riemann Sum that describes the estimation of…

A: Given: n = 8 f(x) = x2 + 1

Q: Find the average value of f(x)=2sinx+2cosx on the interval [0,17pi/6]. Average value=

A: the average value of f(x)=2sinx+2cosx on the interval [0,17pi/6].

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.