Share
Explore BrainMass

# Integrals

### Line integrals

See attached page Evaluate the line integrals, where C is the given curve

### Integral

See attached page Evaluate the integral by making an appropriate change of variables.

### Integration by Parts and Motion in a Particle

A particle is set in motion at time t=0 and moves to the right along the x-axis. (a) Suppose that its acceleration at time t is a=100e^(-1). Show that the particle moves infinitely far to the right along the x-axis. (b) Suppose that its acceleration at time t is a=100(1-t)e^(-1). Show that the particle never moves beyond a c

### Integration by Parts: Area and Volume

The figure shows the region bounded by the x-axis and the graph of. Use Formulas (42) and (43). Which are derived by integration by parts? To find (a) the area of this region; (b) the volume obtained by revolving this region around the y-axis. Formula (42) Formula (43). See the attached files.

### Integration of the Weibull distribution

I am trying to integrate the attached function ( a version of Weibull distribution). I have the solution in Maple -- I think. But I cannot prove it. Tried Integration by parts but still missing something. Please Integrate with respect to y. If it is not clear from the pdf the function is basically : a/b * y ^ (a-1) * e^(-(y

### Integral for area Bounded by Two Functions

The problem reads: 1)Plot the following functions on the same coordinate system with the given domain and range. y = x^4 - 2x^2 and y = 2x^2 -4 <= x <= 4 -2 <= y <= 10 2)I am then to set up the definite integral that gives the area of the region bounded by the graphs of the functions. I had no trouble plotting th

### Brownian motion and Ito's formula

Hi, I've attached 2 questions in one file. Thanks. Question 1 hints: Hint 1: you have a process Y and a function, the first instinct should be to try Ito. Hint 2: what would the SDE of a martingale look like? Look at attached lecture note. Question 2 hint: Hint: use the integral version of Ito's formula.

### Reimann Sum

1. Write a Reimann sum and then a definite integral representing the volume of the region, uisng the slice show. Evaluate the integral exactly. ... 2. Find the volume of a sphere of radius r by slicing. ... [See attachment for questions.]

### Work Done by Vector Field Along Helix and Straight Line

#4 in attached problem set (see attachment). 4. Find the work done by the force field F(x, y, z) = -zi + yj + xk in moving a particle from the point (3, 0, 0) to the point (0, pi/2, 3) along: (a) a straight line (b) the helix x = 3cos(t), y = t, z = 3sin(t).

### Integrated integral for volume of a unit cube

Give an iterated integral describing the volume of a unit cube (side length 1) in cylindrical and spherical coordinates.. I just need the integral and a short explanation, I do not need them solved.

### application of triple and double integrals

See the attached file for full description. 26. Evaluate the triple integral, where E is bounded by the planes y = 0, z = 0, x + y = 2 and the cylinder y^2 + z^2 =1 in the first octant. Find the volume of the given solid 30. Under the surface z = x^2y and above triangle in the xy-plane with vertices (1, 0), (2, 1), and (4

### Volume of solid, triple integral, sperical coordinates

Use spherical coordinates (iterated triple integral) to find the volume of the solid in the first octant whose shape is determined by the graph of the cone z=sqrt(x^2+y^2), the cylinder x^2+y^2=1 and the coordinate planes. NOTE: Please see attachment for original problem (question #4)and work i have done on it so far.

### Basic Mathematics Problems Involving Digits and Word Problems

Find the greatest common factor for the following group of numbers: 24, 36, 48 A rectangular picture window is 5ft by 8ft. Polly wants to put a trim molding around the window. How many feet of molding should she buy? (Can you draw a picture?) Write the following in standard form of a number (Hint: use a number char

### Integrals, Vector Fields, and Differential Equations

Please see attached 1) To find the general integral of the differential equation, discuss existence et uniqueness and find the particular integral that passes for the point (1;5/2) 2) Considering the linear equation of the 2nd order z'' - (2/x) z' + (2/ x2)z = 10 / x2 , x > 0 .

### Learning to Sketch Areas under the Standard Normal Curve

Sketch the areas under the the standard normal curve over the indicated intervals, and find the specified areas. 14. To the left of Z = 0.72 18. To the right of Z = -2.17 24. Between Z = -1.40 and Z = 2.03 34. P (z &#8804; 3.20) 42. P (-1.78 &#8804; z &#8804; -1.23) 46. P (-2.37 &#8804; z &#8804; 0)

### Integration and other topics

See attachment for fomatting 1 Evaluate 3&#8747;1 1-&#8747;-2 (x2y-2xy3)dydx 2 Correctly reverse the order of integration, then evaluate 1&#8747;0 1&#8747;y xeydxdy 3 The plane region R is bounded by the graphs of y=x and y=x2 . Find the volume over R and beneath the graph of f(x, y) = x + y. 4 Find t

### Definite integrals: Solving for area under a curve? (See the attached question file)

(See the 2 graphs in the attached question file) I need to solve for the area under the 2 noted curves. In the first graph, the beginning x,y coordinate is 0 minutes; 80 degrees F; the ending x,y coordinates are 4.5 minutes; 212 degrees F In the second graph, the beginning x,y coordinate is 5.0 minutes; 213 degrees; th

### Line integral evaluation directly and by Green's Thorem

See attached page for problem. Evaluate the line integral by two methods, directly and Green's Theorem integral_c (x + 2y)dx + (x-2y)dy C consists of the arc of the parabola y=x^2 from (0, 0) to (1, 1) followed by the line segment from (1, 1) to (0, 0)

### Application of Derivative and Evalution of Integral

1. find dx/dt of x= sqrt(1+cot(3t)). 2. f(x)=(x-2)^2*(x+3)^2, find the interval on which the function f(x) is increasing and decreasing. sketch the graph of y=f(x), and identify and local maximum or mininmum and golobal extrema. 3. f(x)= x^2/(x-1) sketch the graph, identify all extrema, inflection points, intercepts, and a

### An example of contour integration using Cauchy's formula

Evaluate the contour integral of z^2/(4-z^2) around the circle |z+1|=2. The question is attached in correct mathematical notation, along with the student's (incorrect) initial attempt. You will need to refer to this initial attempt when reading the solution.

### Integration Determination

4A) Determine the integral x /(square root of x^2+4) dx by u substitution. 4B) Determine the integral dx /(square root of x^2+4) 4C) Determine the integral dx / x^2+4

### Work done to pump all water over the edge of the trough

A 10-ft trough filled with water has a semicircular cross section of diameter 4 ft. How much work is done in pumping all the water over the edge of the trough? Assume that the water weighs 62.5lb/ft^3.

### Wave Equations and Periodic Differentiable Functions

3. Solve the wave equation, &#8706;2u/&#8706;t2 = c2(&#8706;2u/&#8706;x) -&#8734; < x < &#8734; With initial conditions, u(x,0) = (1/x2+1)sin(x), and &#8706;u/&#8706;t(x,0) = x/(x2+1) 4. Suppose that f is a 2&#1087;-periodic differentiable function with Fouier coefficients a0, an and bn. Consider the Fourier coeffici

### Integrals, Area under the Curve and Solid of Revolution

1. Evaluate: &#8747;2cos2 xdx 2. Figure 12.1 y = 9-x2 , y=5-3x Sketch the region bounded by the graphs of Figure 12.1, and then find its area. 3. Figure 13.1 1?0x4dx Approximate the integral (Figure 13.1); n=6, by: a) first applying Simpsonfs Rule and b) then applying the trapezoidal rule. 4. Find

### R is bounded below by the x-axis and above by the curve

1)Figure 11.1: 0<=x<=(pie)/2 R is bounded below by the x-axis and above by the curve y = 2cos(x), Figure 11.1. Find the volume of the solid generated by revolving R around the y-axis by the method of cylindrical shells. 2)Figure 15.1: y= 1/(x^2+4x+5) R is the region that lies between the curve (Figure 15.1) and t

### convergence of improper integral

See attachment and show work. 1. Find a function f(x) = x^k and a function g such that f(g(x)) = h(x) = (3x + x^2)^0.5; 2. Express the distance between the point (3, 0) and point P(x, y) of the parabola y = x^2 as a function of x 3. Determine whether converges or diverges. If it converges, evaluate the integral

### Integrals and differentiation

Differentiate the function f(x) = ln(2x + 3). Find . lim e^ 2 x/(x+5)^3 &#8594;&#8734; Apply l'Hopital's rule as many times as necessary, verifying your results after each application. Evaluate &#8747; x sinh(x)dx . Determine whether 2 &#8747; (x / ^(4-x^2)) (dx)

### Implicit differentiation, integral, maximum area

Use implicit differentiation to find an equation of the line tangent to the curve x3 + 2xy + y3 = 13 at the point (1, 2). What is the maximum possible area of a rectangle inscribed in the ellipse x2 + 4y2 = 4 with the sides of the rectangle parallel to the coordinate axes? 3 . Evaluate &#8747; dt / (t+1)^

### Integration

Evaluate &#8747;3x+3 / x^3-1 (dx) Use trigonometric substitution to evaluate &#8747;1 / ^/¯1+x2(dx) Determine whether converges or diverges. If it converges, evaluate the integral. &#8734;&#8747;-&#8734; 1 / 1+x2 (dx)

### Integrals

Evaluate &#8747;(^/¯x+4)^3 / 3^/¯x(dx) &#8747;x2sin2x dx &#8747; sin5xdx