Simpson's Rule
Question 1: What is the exact value of ∫ 0-->2 x^3 + 3x^2 dx ? Question 2: Find SIMP(n) for n = 2, 4, 100. What is noticeable? ---
Integrals
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Integration using left, right, trapezoid, and midpoint rules
(See attached file for full problem description) Definite integrals 1. Show geometrically why int sqrt (2-x^2) dx = pi/4 + 1/2 2. Approximate int sqrt (2-x^2) dx for n = 5 using the left, right, trapezoid, and midpoint rules. Compute the error in each case using the answer to question 1 to compare the errors
Approximating Definite Integrals
See the attachment for the graph and integral in this question on approximating the area under a curve using the left, right, trapezoid and midpoint Riemann sums.
To solve several definite and indefinite integrals.
Please see the attachment for the questions. Please solve each problem step by step giving solutions please. SHOW every step getting to the answer. Show substitutions, etc. DO NOT SKIP STEPS PLEASE! Look below for attachments. Adult student asking for help and I learn by the examples you solve. I learn different than ot
Calculus Integration by Parts
Please evaluate the following integral using the formula for integration by parts, int (udv) = uv - int (vdu) Int z(ln z)²dz
Integration ( Integrate ) by Parts and Substitution
Please evaluate the following integral using the formula for integration by parts, ∫udv = uv - ∫vdu ∫e^(-2x) sin2xdx Please show detailed solution, including substitution(s) used.
Integration ( Integrate ) by Parts and Substitution : ∫2xsin‾¹(x²)dx
Please evaluate the following integral using the integration by parts formula: ∫udv = uv - ∫vdu for the integral ∫2xsin‾¹(x²)dx and then evaluate for the limits 0≤x≤1/√2 Please show all the steps for the integration and substitution.
Integration (Integrate ) by Parts : ∫ 2x sin-¹(x²)dx
Evaluate the following integral using integration by parts and the formula: ∫udv = uv - ∫vdu ∫ 2x sin-¹(x²)dx Please show each step in the solution. Thank you
Integration (Integrate) by Parts
Evaluate the following integral using integration by parts and the formula: ∫udv = uv - ∫vdu ∫t² e^4t dt.
Integration ( Integrate ) by Parts : ∫(r² + r + 1)e^r dr
Evaluate the following integral using integration by parts and the formula: ∫udv = uv - ∫vdu ∫(r² + r + 1)e^r dr Please show each step in the solution. Thank you
Integration by Parts: integral(p^4)(e^-p) dp
Evaluate the following integral using integration by parts and the formula: integral udv = uv - integral vdu integral(p^4)(e^-p) dp Please show each step in your solution. Integrate.
Evaluate the Integral : ∫1/(4-z^2)^3/2 dz
Calculate the integral. If you use software to complete it, explain to me what steps are needed to find the solution, (I can easily input the problem into Maple myself). Please see the attached file for the fully formatted problem. integrate, integration
Integration with Partial Fractions
Calculate the following integral and show all the steps (the S represents the integration symbol): S ((y + 2 ) / ( 2y^2 + 3y + 1 )) dy
Complete the square and give a substitution which could be used to compute the integral of 1/ (x^2 + 2x +2). (see equation in attachment)
Complete the square and give a substitution which could be used to compute the integral of 1/ (x^2 + 2x +2). (see equation in attachment)
Solve
Solve. Show all the steps. If you use software to complete it, explain to me what steps are needed to find the solution, (I can easily input the problem into Maple myself). (see equation in attachment)
Complete explanation of integration problems
Solve. Show all the steps. If you use software to complete it, explain to me what steps are needed to find the solution, (I can easily input the problem into Maple myself). integral (1/(cos^4)7x)dx
Integrate
Solve. Show all the steps. If you use software to complete it, explain to me what steps are needed to find the solution, (I can easily input the problem into Maple myself). (see equation in attachment)
Integration by parts
In this problem I am asked to use integration by parts utilizing the formula: ∫udv = uv - ∫vdu Please show the values of u, dv, du, and v and each of the steps to achieve the solution. This problem may involve more than one sequence in integrating by parts. Thank you. ∫4xsec²2xdx
Integration by parts
In this problem I am asked to use integration by parts utilizing the formula: ∫udv = uv - ∫vdu Please show the values of u, dv, du, and v and the steps to achieve the solution. Then show the final value after substitution of the limits. Thank you. ∫x³lnxdx 1≤x≤e
Integration by parts
In this problem I am asked to use integration by parts utilizing the formula: ∫udv = uv - ∫vdu Please show the values of u, dv, du, and v and the steps to achieve the solution. Thank you. ∫x²sinx dx
Surface Area of a Revolving Curve
Using the formula for the surface area of a revolving curve about the y-axis: S=∫2Ï€x√(1 + (dx/dy)²)dy throughout a,b Find the area of the surface generated by revolving the curve about the y axis within the given boundaries x=√(2y-1) 5/8≤y≤1 the revolving base passes thru the point (1/2
Surface Area of a Revolved Curve
Utilise the following formula that gives the surface area of a curve that revolves around the y-axis: S=∫2πx √ (1 + (dx/dy)²)dy throughout c, d Now calculate the area of the surface that would come about by rotating the curve around the y axis with the boundaries below: x = (1/3)y³'² - y ¹'² 1
Surface area of revolving curve
Using the formula for the surface area of a revolving curve about the x-axis: S=∫2πy√(1 + (dy/dx)²)dx throughout a,b Find the area of the surface generated by revolving the curve about the x axis within the given boundaries y=√(x + 1) 1≤x≤5 Please be detailed, showing the compl
Length of a curve
Using the formula for the length of a curve y=f(x) from a to b L=∫√(1 + (dy/dx)²)dx Find the length of the curve: x=(y³′²∕3)- y¹′² from y =1 to y=9 Hint: 1 + (dx/dy)² is a perfect square.
Integrating to find length of a curve
Using the formula for the length of a curve y=f(x) from a to b L=∫√(1 + (dy/dx)²)dx Find the length of the curve: y=x³′² from x=0 to x=4
Shell method of finding volume of revolving solid
The following curve and line define the boundaries of a solid generated by revolving it around the x axis. Using the shell method, find the volume of the solid y=√x y=0 y=2-x
Shell method of finding volume of revolving solid
Using the shell method, find the volume of the solid generated by revolving the region bounded by the curve and line below about the x-axis. x=2y-y² x=y
Integration in Finding the Volume of Rotated Solid
Determine the limits of integration and then Find the volume of the solid generated by revolving the region bounded by the line and curve about the x-axis: y=4-x² y=2-x Using the formula V=∫π[R(x)]²dx
Area between two curves
The area I am looking for is the region bounded by the two functions y=x² and y=2-x between the limits (2,0) and (0,0) and bounded by the x axis and the point y=1 What is the area between these two curves? Using the formula A=∫f(x)-g(x)dx
Riemann sum area between two curves
Using the Riemann sum formula: A = ∫ [f(y) - g(y)]dy from a to b Find the area between the two curves x=12y²-12y³ and x=2y²-2y. The y limits are 1 and zero. Please show a detailed solution. Thank you.