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# Integrals

### Integral Differential Equation

Please help working on these problems Please show all steps. Section 7.7 # 18 See attached Solve the given integral equation or integro-differential equation.

### Integration by parts - Use integration by parts to compute

Use integration by parts to compute the following definite integral: &#643; (e = upper limit of integration & 1 = lower limit of integration) x^4 ln(x) dx (Please see attached document)

### Definite Integration Substitution Factors

Compute the following definite integral: ___ ____ Integration limits: 1<x<2 Function to integrate: exp[sqrt(x+1)] / sqrt(x+1) see file for better representation.

### Partial Fraction Decomposition and Integral

See attachment. Compute the following definite integral using partial fraction decomposition: ʃ˳ˡ 5x - 2 / (x^2 - 8x + 12) (see attached file) that's a 1 for upper limit and 0 for lower limit).

### Integration by parts integrals

See attachment Use integration by parts to compute the following definite integral: &#643; (0 is the lower limit of integration & 1 is the upper limit of integration) t ln (2t + 1) dt Hint: Make sure that you keep in mind that t is the independent variable

### Initial Value an Derivation of Parameters

Please show all steps to solution. Solve the initial value problem Where in three different ways. 1) Using the method of variation of parameters .You can use any standard table of integrals to perform any of the integrals required in the solution. See the attached file.

### Integrable function proof

Assume that fn->f uniformly on [a,b] and that each fn is integrable. Then f is integrable and lim n->inf of the integral from a to b of fn = integral from a to b of f

### Evaluating Integrals with Green's Theorem

Use Green's theorem to evaluate the line integral along the given curve. I will be using the S sign to portray the integral sign. 1) S_c F*dr where F(x,y) = (y^2 - x^2 y)i + xy^2 j and C consists of the circle x^2 + y^2 = 4 from (2, 0) to (sqrt(2), sqrt(2)) and line segment from ( sqrt(2), sqrt(2) ) to (0, 0) and from (0,

### Proving a Ring is A Domain

1. a. Is R= {a+b(squareroot of 2): a,b element of Z} a domain? b. Using the fact that alpha= (1/2)(1 + (square root of -19)) is a root of ((x^2)- x + 5), prove that R={a + b(alpha) : a,b element of Z} is a domain. Z= integers 2. Assume that (x-a) divides f(x) in R[x]. Prove that (x-a)^2 divides f(x) if and only if (x-a)

### Integral Straight Line or an Arc

Evaluate integral C (y^2 + 1) dx + 2xy dy; (a) C is the straight line from (-1; 0) to (1; 0). (b) C is the arc of the circle x^2 + y^2 = 1 going counter-clockwise from (-1; 0) to (1; 0).

### Volume by Cylindrical Shells, Disks and Washers

First, I can't tell the difference between the two. Both seem to indicate a region bounded by two or three certain functions or points. I was wondering if anyone could give a step by step explanation of how to do 1. Volumes by Cylindrical Shells 2. Volumes by Disks and Washers.

### Numerical Analysis Problem using Matlab

Write a function to calculate the integral from a to b of f(x) dx using the composite trapezoid rule with n equal subunits. test the code on a) the integral from 0 to pi of sin(x), b) the integral from 0 to 1 of exp(x) and c) the integral from 0 to 1 of arctan(x). Provide the codes used and all the results and work.

### Evaluating a Line Integral

Please see my attached pdf and thank-you for your assistance. Evaluate the line integral.

### Explaining Complex Integration

Please see file attached... (z,r) is a circular contour of radius r>0 centred at z Explain why. cannot be evaluated by applying Cauchy's integral formula with , when = 1. Hence evaluate the integral.

### Evaluating indefinite and definite integrals

See attached file for full problem description. Please show in detail how to solve the following integral. (a) Please show in detail how to solve the following indefinite integral. (b) Thank you.

### Complex Integration

Help required on how to do the following: to evaluate : integral (z+i)/(z+2i) dz where curve is semicircle from 0 to 4i, initial point 0 and where curve is circle |z-2i|=2 anticlockwise.

### Evaluate the definite integral using substitution methods

Lower limit = 0 upper limit =square root of Pi Evaluate the definite integral x*cos(x^2) dx

### Evaluating a Definite Integral

Lower limit = 0 upper limit = 5 Evaluate the integral ∫ (2e^x + 4cosx) dx.

### An Explanation for a Line Integral

Please address the following question: Show that the line integral is independent of path and evaluate the integral. Integral_c (2y^2 - 12x^3y^3)dx + (4xy - 9x^4y^2)dy C is any path from (1, 1) to (3, 2)

### Change of Variables in Double Integral

Please see the attached file for the fully formatted problem. Calculate SSR 1/(x+y) dydx where R is the region bounded by x=0, y=0, x+y =1, x+y=4, by using the mapping T(u,v) = (u-u-uv, uv).

### Complex integration solution

Please show all steps to solution. Let . Evaluate the integral dz Where &#947; is the unit circle.

### Area under a curve.

Please see attached file. I need to determine the area under each of the curves in red --- I have fitted a curve using Excel to derive the polynomial equation. In the first graph, the x-axis limits are 0 and 4.5; in the 2nd curve, the x-limits are 0 and 5.0. The units for the x-axis is time (minutes) and the y-axis is p

### Line integrals

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

### Solving a Double Integral

Please see the attached JPEG. Thank-you so much for your expertise. Computer the double integral over region D. where f(x,y) = y^2 * sqrt(x); and D is the set of (x, y) where x > 0, y > x^2, and y < 10 - x^2.

### Vector Calculus: Solving a Double Integral

Please see the attached JPEG file. Find the following double integral (see attached file).

### Integral

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

### Variable substitution in multivariate Integrals

Please see the attached file for the fully formatted problems. calculate the integarl of (3x + 4) over the region bounded by the lines y =x, y = x-2, y =-2x and y = 3 - 2x; Use: x = 1/3(u+ v), y = 1/3(v - 2u)

### The Volume of a Sphere Wedge

Find the volume of the smaller wedge cut from a sphere of radius (a) by two planes that intersect along a diameter at an angle of pi/6. Use cylindrical or spherical coordinates, whichever seems more appropriate.

### Evaluate the indefinite integral by parts

See attached Find the indefinite integral using each specified method. Then write a brief statement explaining which method you prefer. x (square root of 4-x) dx (a) By parts, letting dv = square root of 4-x (b) By parts, letting u = square root of 4-x

### Indefinite Integral Examines

Please see the attached file. Find the indefinite integral. (HINT: integration by parts is not necessary in all cases in this section) (integral math sign) x/(square root of x-1) dx I hope you can understand this problem...I don't know how to type in some of the math symbols...if you know let me know and I will rewrite