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
Integrate the following: y = (x - x^2)/(x^(1/6))
Please see the attached file for the fully formatted problem. Integrate:
Use an iterated integral to find the area of the region: y = 1 /sq root (x - 1)
Please see the attached file for the fully formatted problem. Use the indicated change of variables to evaluate the double integral: SR S 60xy dA x = 1/2(u + v) y = -1/2(u - v)
Find the indefinite integral (3-x)/sq root of 9-x^2 dx(dx would be in the numerator). I tried to split this problem apart. First part was: The integral of 3/sq root of 9-x^2 dx and found 3 arcsin x/3 + C, then Second part was: The integral of -x/sq root of 9-x^2 dx and found -3/4 -x + C. I then put them back together to ge
Note: If you have already answered this exact question please do not answer it again. I would like an answer from a different T.A. Thanks Say abs = absolute value. Suppose that the function f:[a,b]->R is Lipschitz; that is , there is a number c such that: abs(f(u) - f(v)) <= (c)abs(u-v) for all u and v in [a,b]. Let P
Apply Green's Theorem to evaluate the integral over C of 2(x^2+y^2)dx + (x+y)^2 dy, where C is the boundary of the triangle with vertices (1,1), (2,2) and (1,3) oriented in the counterclockwise direction. Also check the result by direct integration. Please show detailed working so I can follow the steps of the working.
Find the indefinite integrals (anti-derivatives):
Let f: [a,b] mapped onto Reals be a nonnegative function that is integrable over [a,b]. Then the integral from a to b of f = 0 if and only if greatest lower bound of f (I) = 0 for each open interval I in [a,b].
Please see the attached file for the fully formatted problems. Sketch the curve r = 5 - 3cos(theta) and set up double integral for bounded area in the third quadrant.
Evaluate the following indefinite integral. int[(x^a)sqrt(r+tx^(a+1))]dx, (t not=0, a not=-1). (See attachment)
1) Evaluate the triple integral e^(1-(x^2)-(y^2)) dxdydz with T the solid enclosed by z=0 and z= 4-(x^2)-(y^2) 2) Find the volume of the solid bounded above and below by the cone (z^2) = (x^2) + (y^2), and the side by y=0 and y= square root(4-(x^2)-(z^2))
Please see the attached file for the fully formatted problem. Construct the quickest method to calculate the Laplace Integral. I = S e^(-x^2) dx infinity --> infinity
Questions on integration, see attachment.
Use the integral test to determine the convergence or divergence of the series: En=1 2 / (3n + 5)
Integral x-1, divided by x to the 3rd + x squared to dx. x-1 ----- X to the 3rd + X to the 2nd ( all dx)
For problem #1, its the integral from o to infinity (the symbol for infinity for that problem was cut off)
I'm taking a DE calculus class and I'm having problems figuring out the logic in solving some of the problems. The given integral is improper because both the interval of integration is unbounded and the integrand is unbounded near zero. Investigate its convergence by expressing it a sum of two intergrands-one from 0 to 1 an
Evaluate the double integral Transform the double integral of (i) using plane polar coordinates Show that the 3 x 3 determinant See attached file:
Please see the attached file for the fully formatted problems. Evaluate the following integrals. S (4x^3 -2x - (2/x^3) dx S (1/2x^1/2) dx 1-->0 S ln x dx
The steps for integrating sin or cos to an even power greater than 2 are shown using the example Ssin^4(x)dx.
The steps for integrating an ln standing alone are shown using the example Slnxdx. The same procedure can also be used for integrals of lns that can be simplified using the properties of logs such as ln3x, ln(x^2) or ln(square root of x), or if the entire ln is raised to a power.
I am trying to integrate e to a variable power times sin or cos using integration by parts, but I seem to be going in circles. How is this problem solved? The trick for solving e times sin or cos is shown using the example Se^x*sinxdx.
The steps of U substitution are explained using the example S(3x)/(5x^2-2).
How do I integrate cos^2(x)? Please help me with this and include explanations so I can understand it.
U substitution is explained using the example S4x(x^2+1)^5dx without and with limits of integration.
What am I doing when I integrate a function? (with no numbers at the top and bottom of the integration symbol)
Integration is explained using the example Sx^2dx.