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Evaluate integate (3sin2x - 2cos3x)dx a=pi/4 and b=pi/2

Definite Double Integral

Evaluate the attached integral: a) Write an equivalent iterated integral with the order of integration reversed. b)Evaluate this new integral and check that your answer agrees with part (a)

Double Integrals

Please see the attached file for full problem description. --- Find the volume of the region that lies under the graph of the paraboloid z = x^2 + y^2 + 2 and over the rectangle R = {(x, y) | -1 and in two ways (a) by using Cavalieri's principle to write the volume as an iterated integral that results from slicing

Integration: The Limit of a Sum

Find by the method of summation the value of : a) The integral (from 0 to 1) of the square root of x. (dx) b) The integral (from 1 to 4) of 1 divided by the square root of x. (dx) Please view the attachment for proper formatting.

Cauchy's Formula

See Attachment for equation We know that sin z and cos z are analytic functions of z in the whole z-plane, what can we conclude about *(see attachment for equations)* in the first quadrant

Integration as the limit of a sum

Find the integral by the method of summation the values of :- (a) integral of e^(-x) where the range of integration is from a to b. (b) integral of e^(kx) where the range of integration is from a to b.


Please help with various Calculus questions. (please see attachment)

Improper Integrals surface area problem..

Use l'hopital's rule if needed. Show all work step by step. Use proper notation please. Surface Area: The region bounded by [(x-2)^2]+y^2=1 is revolved about the y-axis to form a torus find the surface area of the torus. PLEASE show or explain step by step process.

Work in joules

A trough is 2 meters long, 2 meters wide, and 2 meters deep. The vertical cross-section of the trough... (See attached)

Finding a centroid

Find the centroid of a two dimensional shape that is formed by the intersection of the lines: y = x-3 and y = x^2

Partial Derivative and Double Integral

The problems are attached 1 -5 based on Chapter Partial Derivative - (Maximum & Minimum Values and Lagrange Multipliers 1. Locate all relative maxima, relative minima, and saddle points of the surface defined by the following function. 2. Consider the minimization of subject to the constraint of (a) Draw the

Revolutions of integrals - astroids

If f(θ) is given by: f(θ)=6cos^3θ and g(θ) is given by: g(θ)=6sin^3θ Find the total length of the astroid described by f(θ) and g(θ). (The astroid is the curve swept out by (f(θ), g(θ)) as θ ranges from 0 to 2pi)

Revolutions of integrals - torus

The circle x=acost, y=asint, 0≦t≦2pi is revolved about the line x=b, 0<a<b, thus generating a torus (doughnut). Find its surface area. Area if the torus:_____________.

Rotation of integrals

Find the volume of a solid generated by revolving about the x-axis the region bounded by the upper half of the ellipse *See attached for equation* and the x-axis and thus find the volume of a prolate spheroid. Here a and b are positive constants, with a<b Volume of the solid of revolution: Please see attachment for det


Show that the integral from 0 to infinity of (t^n e^-t dt) = n!


See attached for Diagram The base of a certain solid is the area bounded above by the graph of y=f(x)=16 and below by the graph of y=(gx=36*. Cross sections perpendicular to the x-axis are squares. See picture above. Use formula (see attachment) to find the volume of the solid.


Find the volume of the solid obtained by rotating the region bounded by the given curves: y=1/x^6, y=0, x=4, x=8 about the "y" axis


Find the volume of the solid formed by rotating the region inside the first quadrant enclosed by: y= x^4 y= 125x about the x-axis. I am more concerned with understanding than the answer. Thanks for your help.


If f(x) = int_{1}^{x^{2}} t^2dt then f'(x)= then f'(5)=

Evaluate the integral

The following expression describes the total electric current to pass in the circuit please see attached


Decide whether to integrate with respect to "X" and "Y", then find the area of the region. x+y^2=42, x+y=0.

Integral domain

There is integral domain with exactly six elements. Disprove or Prove

MATLAB Programming

Develop a program (M-File) called 'integrate' that will perform a first-order numerical approximation, yi(t), of the running integral with respect to time of an array of experimental data y(t). The M-File must also perform another first order approximation, yi2(t), of the first integral resulting in a double integration of the