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Integrals

Multivariable Calculus : Iterated Integral

( f ^n_r means that n is on the top of the f and r is on the bottom) Evaluate the iterated integral: f ^(pi/2)_0 f ^(pi/2)_0 cos x sin y dy dx f: is the integral symbol

Multivariable Calculus: Triple Integral - Cylindrical Coordinates

Question: Solve by triple integration in cylindrical coordinates. Assume that each solid has unit density unless another density function is specified: Find the volume of the region bounded above by the spherical surface x^2 + y^2 + z^2 = 2 and below by the paraboloid z = x^2 + y^2.

Multivariable Calculus : Triple Integral

Compute the value of the triple integral   _T f(x, y, z) dV: f(x, y, z) = xyz; T lies below the surface z = 1 - x^2 and above the rectangle -1*x*1, 0*y*2 in the xy-plane. : is the integral symbol

Multivariable Calculus : Integral

Please show all work; don't explain each step. Please DON'T submit back as an attachment.Thank you. (  ^n_r means that n is on the top of the  and r is on the bottom) Sketch the region of integration, reverse the order of integration, and evaluate the resulting integral:  ^1_0  ^1_y

Equations

Show that there are exactly four distinct sets of integers which satisfy the attached equations:

Differential Equation

Given dy/dx= -xy/(ln y), where y>0 find the general solution of the differential equation What solution satisfies the condition that y=e^2 when x=0... express in y=f(x) Why is x=2 not in the domain found from that?

General calc problems

20) If the function f is continuous for all real numbers and lim as h approaches 0 of f(a+h) - f(a)/ h = 7 then which statement is true? a) f(a) = 7 b) f is differentiable at x=a. c) f is differentiable for all real numbers. d) f is increasing for x>0. e) f is increasing for all real differentiable ans is B. Explain

Arc Length

Evaluate the integral in the attached file "Arc Length.doc" for arc length (L). The intent is to solve for a numerical answer and the values for a, b, and t are all constant.

Solving an integral

Can you show me the solution to this integral? See attached file for full problem description.

Integral

Can you please show all the working to solve the attached integral?

Transformation

Please see the attached file for full problem description. --- Use a transformation to evaluate the double integral of f(x,y) given by f(x,y)=cos(2x+y)sin(x-2y). over the square region with vertices at (0,0) P(1,-2) Q(3,-1) & R(2,1) (My notes from class-uses substitution, change of variables) Solution. Letting

Double Integral

Can anyone please show me how to solve these double integrals, with a step by step approach. I know the answer is 63 - but Ive tried so many times & I don't know where I'm going wrong. upper limits are 1&y=2 x+4y^2 dydx + lower limits are -2&y=-x upper limits are 4 & y=2 x+4y^2 dydx lower limits ar

Double Integral over a Square Region

Use a transformation to evaluate the double integral of f(x,y) given by f(x,y)=cos(2x-y)sin(x+2y) over the square region with vertices at (0,0) (1,-2) (3,-1) & (2,1) (My notes from class-uses substitution, change of variables) I have let u=(2x-y) & v=(x+2y) using substitution (change of variables)

Population model

In some populations, the amount of births is directly proportional to the population at any given point in time and the amount of deaths is directly proportional to the square of the population at any given point in time. 1. Write an equation that models the change in a population that fits the above description. Make sure t

Integrate

Please see the attached file for full problem description.

Integrating factors

Using: d tan^-1 (x/y)=(y dx - x dy)/(x^2 + y^2), and ½ d ln(x^2 + y^2)=(x dx + y dy)/(x^2 + y^2) find integrating factors for, and solve, the following equation: (2x^(2)y + 2y^3 - x) (dy/dx) + y=0

Solve a Complicated Integral

Show that (7x/x^2 + 5) + (4/3x+15) - (5/6x-24) = (45x^3-15x^2-825x-35)/((6x^2+30)(x^2+x-20)) then use that information to determine S=integral S(45x^3-15x^2-825x-35)/((6x^2+30)(x^2+x-20)) dx.

Partial Fraction Decomposition

Please see the attached file for the fully formatted problems. Partial fraction decomposition is a technique used to convert a fraction with a polynomial numerator and a polynomial denominator into the sum of two or more simpler fractions. It eases integration by reducing it to the sum of integrals, each of which will most l

Volume of Revolution

1. The shaded region R, is bounded by the graph of y = x^2 and the line y = 4. a) Find the area of R. b) Find the volume of the solid generated by revolving R about the x-axis. c) There exists a number k, k>4, such that when R is revolved about the line y = k, the resulting solid has the same volume as the solid in par

Integration

Integrate the following: y = (x - x^2)/(x^(1/6))

Integration

Please see the attached file for the fully formatted problem. Integrate: