### Surface Area of Revolution

Find the surface area of revolution generated by revolving the region under the curve y=2x on the interval [0,1] about the x-axis.

Explore BrainMass

- Anthropology
- Art, Music, and Creative Writing
- Biology
- Business
- Chemistry
- Computer Science
- Drama, Film, and Mass Communication
- Earth Sciences
- Economics
- Education
- Engineering
- English Language and Literature
- Gender Studies
- Health Sciences
- History
- International Development
- Languages
- Law
- Mathematics
- Philosophy
- Physics
- Political Science
- Psychology
- Religious Studies
- Social Work
- Sociology
- Statistics

Find the surface area of revolution generated by revolving the region under the curve y=2x on the interval [0,1] about the x-axis.

Determine if the following equation is exact. If it is, solve it. If not, try to solve it by finding an integrating factor. cosx + y(sinx)y'=0

8. Heat Equation with Circular Symmetry. Assume that the temperature is circularly symmetric: u u(r,t), where r^2 x^2 | y^2. Consider any circular annulus a ≤ r ≤ b. a) Show that the total heat energy is r π f^b_a cpurdr. b) Show that the flow of heat energy per unit time out of the annulus at r b is: (see attachment

6. Let g be a primitive root of m. An index of a number a to the base (written ing a) is a number + such that g+≡a(mod m). Given that g is a primitive root modulo m, prove the following... 7. Construct a table of indices of all integers from.... 8. Solve the congruence 9x≡11(mod 17) using the table in 7. 9.

∫arctan x/[(x^2)+1] dx

∫2x/(x^2 + 1) dx

Find the area of the region 1.) y=x- x^2 points (0,1/4) (1,0) 2.) y=1/x^2 points ((1,1) (2, 1/2) Find and evaluate the integral 1.) integral 1 to 0 2xdx 2.) integral 0 to -1 (2x +1)dx 3.) integral 1 to -1 (2t -1)^2 dt 4.) integral 5 to 2 (-3x +4) dx 5.) integral 4 to 0 1/sq rt 2x +1 dx 6.) integral 2

1.) You are shown a family of graphs each of which is a general solution of the given differential equation. Find the equation of the particular solution that passes though the indicated point. dy/dx=-5x-2 point (0,2) 2.) Find the cost function for the marginal cost and fixed cost marginal costs fixe

Consider the integral... Please see the attached file for the fully formatted problems.

Given that the general solution to the wave equation in one space dimension is given by where f, g are arbitrary twice continuously differentiable functions deduce that the solution s satisfying the initial conditions and for some function v, is (this is a special case of the so called D'Alembert's solution of

Evaluate the integers. Please see attached.

Find the area of the surface generated when the arc of the curve... between t=0 and y=1 is revolved about: a) the y-axis b) the x-axis c) the line y= -1 Please see attached for all twelve questions (circled problems).

Find the volume of the solid obtained by rotating the region bounded by the given curve about the specific line. (a) y=e^{5x}, y=0, x=0, x=1, about x -axis (b) x=5y-y^2, x=0, about y -axis"

In a certain city the temperature at t hours after 9 A.M. is approximated by the function T(t)=44+12sin(pi(t))/12). What is the average temperature of the city during the period from 9 A.M. to 9 P.M.?

Consider the region enclosed by the curves 2y=4sqrt{x}, y=5, 2y+4x=8. [Note: the y-axis is not a boundary of this region.] Decide whether to integrate with respect to x or y. What is the area of the region?

Find the numbers b such that the average value of f(x)=2+6x-3x^2 on the interval [0,b] is equal to 3.

Compute the integral from 0 ---> infinity. e^(-st)*(1/2)*t^2*e^-t+17*t*e^-tdt

Show that if {see attachment} is a continuous random variable then ... Please see attachment for complete list of questions.

There is a rope that stretches from the top of Maidwell building to a tree on the racecourse, and the length of this rope is 1km. A worm begins to travel along the rope at the rate of 1cm each second in an attempt to get to the other end. then a strange thing happens... some malevolent deity intervenes to make life even hard

Evaluate the following integrals: (1)The integral of (6sin[2x])/sin(x)dx=____+C (2)The integral of (7-x)(3+[x^2])dx=____+C (3)The integral from 3 to 7 of ([t^6]-[t^2])/(t^4)dt=____+C (4)The integral of (6sin[x])/(1-sin^2[x])dx=____+C

Thank you in advance for your help. Evaluate the following definite and indefinite integrals: (1)The integral of (2x)/([x^2]+1)dx (2)The integral of [(arctan(x))/([x^2]+1)]dx (3)The integral of sqrt([x^3]+[1x^5])dx (4)The integral of (2+x)/([x^2]+1)dx (5)The integral of (2x)/([x^4]+1)dx (6)The integral from 0 to 2 of (x

Thank you in advance for your help. Evaluate the integrals by making the given substitution: (a)The integral of x(4+x^2)^3dx; (u=4+x^2) (b)The integral of ((sin sqrt[x])/sqrt[3x])dx; (u=sqrt[x]) (c)The integral of e^(3sin(t))cos(t)dt; (u=sin(t))

Thank you in advance for your help. Find the general indefinite integrals: (a)The integral of x(1+2x^2)dx (b)The integral of ((x^2)+1+(2/x^2+1))dx

Water flows from the bottom of a storage tank at a rate of r(t)=200-4t liters per minute, where 0 is less than or equal to t and t is less than or equal to 50. Find the amount of water that flows from the tank during the first 10 minutes.

Consider the definite integral I 4 I = ∫ e^x dx 0 1. evaluate the integral I directly by use of a suitable anti-derivative. 2. evaluate the integral I by use of a suitable Riemann sum and formally limiting that sum 3. evaluate the integral I by use of the trapezoidal rule: a) I T,2 - for 2

Derive an integration rule for the domain [0,1] based on the quadrature points x1=0, x2=1/3 and x3=1, which is exact for polynomials of degree <= 2. Please see attached for full question.

Calculate the following integrals: ∫ from 0 to ∞ x^¼/(x²+9) dx Please see attached for proper format.

Calculate the following integral... Please see attached for full question.

Calculate the following integral: ∫ 0-->2pi e^(e^iθ) dθ Please see attached for full question.

Suppose f(x) is continuous and decreasing on the closed interval (4 is less than or equal to x is less than or equal to 11), that f(4)=6, f(11)=3, and that the integral as 4 goes to 11 of f(x)dx=27.01678. What is the integral as 3 goes to 6 of f^-1(x)dx?