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# Integrals

### Integration by Partial Fractions

Integration by Partial Fractions : &#8747;(2x^3 - 4x^2 + x + 3)/(x-1)^2 dx

### Partial Fractions in Integration

Please display every step to finding the answer to the following (S stands for the integral sign): S 1/ (x^2 + 3x -10) dx

### Indefinite Integral

(See attached file for full problem description) Could someone please help me with the problem and show me ALL the steps.

### Integration by Substitution &#8747;(e^(ln x))/x dx

&#8747;(e^(ln x))/x dx

### Integration by parts

(See attached file for full problem description) Could someone please help me with the problem and show me ALL the steps.

### Find the integral of a polynomial fraction.

Find the integral of a polynomial fraction. See attached file for full problem description.

### Simpson's Rule Explanations

Use problems 8 and 9 on p. 348 as an outline to write a clear explanation why Simpson's rule is a good way to approximate definite integrals over a finite interval. The questions are attached, I need help explaining each step of the problem, with a few different proofs of how this actually works.

### Integration Riemann Sum Functions

Please solve and explain. Write the expression for the Riemann sum of f(x) = x^2 - 4x on the interval [0,8] with n uniform subintervals using the right hand endpoints of the subintervals. Do not evaluate. Using the Reiman Sum, write the definition of the definite integral 8 to 0 (x^2 - 4x)dx. Do not evaluate. Using

### To find the number of monomials of length n, to write a generating function.

Note that the generating function has to be in terms of powers of x. Example: the number of ways to select r balls from a pile of three green, three white, three blue, and three gold balls is the generating function--->(x^0+x^1+x^2+x^3)^4 Here's the problem: 4. In noncommutative algebra, the term monomial refers to any arra

### Integration : Limit and Intervals (4 Problems)

Please see the attached file for the fully formatted problems.

### Integration : Definite Integrals and Geometric Formula to Evaluate the Integral ( 3 Problems)

For the problems attached, please sketch the region whose area is given by the definite integral. Then use a geometric formula to evaluate the integral (a > 0, r >0). Please explain as much as possible.

### 4 Definite Integrals

Evaluate the integrals using the following values (i) For integral 4 on the top, 2 on the bottom x^3 dx = 60 (ii) For the integral 4 on the top, 2 on the bottom x dx = 6 (iii) For the integral 4 on the top, 2 on the bottom dx = 2

### Integration

For the problems attached, please sketch the region whose area is given by the definite integral. Then use a geometric formula to evaluate the integral (a > 0, r >0). Please explain as much as possible.

### Integration of Summation Series and Limits

Please see the attached file for the fully formatted problems.

### Integration : Evaluate the definite integral using the definition of a limit (2 Problems)

Please see the attached file for the fully formatted problems.

### 14 Integration Problems : Adding and Subtracting Integrals, Finding Areas and Evaluating Definite Integrals

Please see the attached file for the fully formatted problems.

### Integration to Determine Given Area

For 21 and 22 on the attached page, please set up a definite integral that gives the area of the region. (Do not evaluate the integral). Please offer as much explanation as possible.

### Volume and integration

Find the region enclosed by x=3y and x=-y^2+4. Set up integrals both shell and disc that represent the volume generated when this region is revolved about y=4. Set it up, do not work to completion.

### Integration using the Midpoint Rule

Please explain and solve the following. Use the midpoint rule with n = 4 to approximate the area of the region bounded by the graph of the function and the x axis over the indicated interval. f(x) = x^2 + 3 [0,2]

### Integration

Please explain how to solve and solve the following problem. Use the limit process to find the area of the region between the graph of the function and the y-axis over the indicated y interval. Sketch the region. f(y) = 3y, 0 is less than or equal to y which is less than or equal to 2

### Integration

Please explain how to solve the following problems and solve the problems. Use the limit process to find the area of the region between the graph of the function and the x-axis over the indicated interval. Sketch the region. 47. y = -2x + 3 [0,1] 49. y = x^2 + 2 [0,1] 53. y = 64 - x^3 [1,4] 55 y

### Integration Sum of Terms

Please explain how to solve the attached problems (as much explanation as possible) and solve to the specified answers. Find a formula for the sum of n terms. Use the formula to find the limit as n approaches infinity.

### Integration of Unit Squares Explanation

Please explain how to do problem 23 on the attached scan. Answer is that the shaded region falls between 12.5 square units and 16.5 square units. As much explanation as possible please. Please also explain how to do 27, 28, 29 and 30 on the attached scan. As much explanation as possible. Please solve the problems. Answer

### Integration for Infinity Approaches

Please explain how to do the following problem. Find the limit of s(n) as n approaches infinity. s(n) = 1/n^2 [n(n+1)/2]

### Find the volume generated when the triangular region enclosed

∫(0 to 1/sqrt(2) x/ sqrt(1-4x^4) dx Find the volume generated when the triangular region enclosed by y=x, y=4, and x=0 is revolved around the y-axis, using the disk method.

### Residues / Integrals - Complex Analysis : integral

Verify the following equation: integral from 0 to pi/2 of ( d theta/ ( a + sin^2 theta) ) = pi/2[a(a+1)]^1/2 if a > 0.

### Integration by substitution : &#8747;(x^3) / (x^4 + 1)^3 dx

Integral(x^3) / (x^4 + 1)^3 dx

### ODE - Method of Variation of Coefficients

ODE - Method of Variation of Coefficients : (X^2)*y''-2y=Sin(lnx)

### Integrate by Partial Fractions : Integral

Integral [(2x^3 - 4x^2 + x + 3) / (x - 1)^2] dx