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# Integrals

### Divergence of Improper Integrals

The integral from 0 to 1 of 6/x-1 dx If I am correct, the answer guide says this one converges but my answer is going to infinity which is diverges. I need to see your steps to compare with mine please.

### Convergence - Series Expanision for Integral

Obtain a series expansion for the integral ∫_0^(1/2)=1/((1+x^4)) dx and justify your calculation. Please see attachment for full problem. This is for an analysis class, so i need to understand how you get the series expansion, so please give details.

### Finding the Integral: Substitution

Find the integral using each method. Integral x * sq. rt 4 + x dx a) trigonometric substitution b) Substitution: u^2 = 4 + x c) Substitution: u = 4 + x d) Integration by parts: dv = sq. rt. 4 + x dx Thanks.

### Evaluate the Double Integral Over the Region: Example Problem

Evaluate the double integral over the region R. Double int. over R (x)(sq. rt. 1-(x^2) dA: R=[(x,y):0<_x<_1, 2<_y<_3 If I set up the integral f(x,y) dy dx isn't the integral with respect to y equal to zero? I am left with the integral from 0 to 1 of f(x,y) dx then I am having issues actually integrating.

### Integration of Polynomials and Trigonometric Functions: 25 Problems

Integrate the following functions: 1. (4x^2-8x+1)dx 2. (9t^2-4t+3)dx 3. (2t^3-t^2+3t-7)dt 4. (1z^3-3z^2)dz 5. (4z^7-7z^4+z)dz 6. (3 square root u + 1square root u)du 7. (square root u^3-12u^-2+5)du 8. (2v^54+6v^14+3v^-4)dv 9. (3v^5-v^53)dv 10. (3x-1)^2dx 11. (x-1x)dx 12. x(2x+3)dx 13. (2x-5

### Solving second order differential equation

Find the general solution of the second order differential equation y'' - y' - 6y = e^-3x This one is quite long winded, and I am pretty sure that I am getting yh right but can't seem to get close to yp. I think this is a D.R.A.E?

### Concepts of Integration

Please solve the following integration application problems. Please provide steps to arrive at final answer. 1. Find the solid of revolution for f(x) = x^2 and g(x) = 1/2 x^3 for x∈[2, 3] 2. What are the coordinates of the centroid for f(x) = x &#8704;∈[0, 2] 3. Integrate x^2 + 3x - 4 / x 4. How much total work is ex

### Definition of a Derivative

Calc Proofs 1) Using the following two functions X and X^2 develop their derivatives using the Definition of a Derivative for three values of "h" h = .1 h = .01 h= .001 and then repeat the calculation in the limit as h->0 2) Using the two functions above, show that the Finite Sum approximation of the area

### Riemann-Stieltjes Integral or R-S integral

If g is constant on the interval [a,b], then any function f is integrable with respect to g and the value of the integral is 0.

### Mathematics - Average Value of the Function

Find the average value of the function over the given interval and all values of x in the interval for which the function equals its average value. Round your answers to four decimal places. f(x)=16-x^2, [-4,4] (x,y)=(_______)(smaller x-value) (x,y)=(_______)(larger x-value) Thanks

### Mean Value Theorem for Integrals

Find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the given interval. (Round you answer to four decimal places. Enter your answers as a comma-separated list.) f(x)= 8 times sq.rt x, [4,9] c=______ thanks

### Reimann integrable problem

If f is a reimann integrable function on [a,b], and if [c,d] is a subset of [a,b], prove that f is reimann integrable on [c,d] hint: if P is any partition of [c,d], P can be extended to a partition P* of [a,b] with ||P*|| <= ||P||. Show that U(f,P) - L(f,P) <= U(f,P*) - L(f,P*)

### Two Reimann Integrable functions

Are these functions Reimann Integrable? I am just learning this topic, so my description may not be accurate. A function is Reimann Integrable if it's Upper Darboux Sums and Lower Darboux suns are equal. Or stated another way, if U(f, P) - L(f, P) < e The two functions are piecewise functions. 1) f(x) = { 0 when x =

### Differential Equation Problem

Part I Check that N(t) = t/(1 +ct) is a solution of the differential equation dN/dt = N^2/t^2. Treat c as an unspecified constant. Part II Use that N(1) = -1 to find c. Then give the solution N(t) corresponding to this initial condition.

### interpretation of double integrals

Let R represent a county in the northern part of the united states, and let S(x,y) represent the annual snowfall at the point (x,y)in R. Give the interpretation of: a. [double integral over R][S(x,y)dA] b. {[double integral over R][S(x,y)dA]}/[double integral over R][dA]

### integration by substitution.

Evaluate double integral: (int from 0 to 1). (int from 0 to cos inverse y). [square root (1 + sin x) dx dy. be sure to include a sketch of the region R in the xy-plane you are integrating over.

### Volume of solid, ellipsoid and an unbounded solid

Find the volume of the solid that is generated by rotating around the indicated axis the plane region bounded by the fiven curves. 1) y=√x,y=0,x=4; The x-axis 2) y= 1/x, y=0, x=0.1,x=1; the x-axis 3)Find the volume of the ellipsoid generated by rotating around the x-axis the region bounded by the ellipse with equation.

### 13 review questions in calculus

The integrals wouldnt paste from word so I had to write them in 1. If an improper integral is found to have a finite solution, then: A) The solution will always be some multiple of &#960;. B) You've done something wrong. C) The function being integrated converges. D) The function being integrated diverges. 2. If f(x) =

### methods of integration and methods of differentiation

Discuss the similarities you found in methods of integration and methods of differentiation with example please

### Solving the Integrals to Solve by Parts

See the attached file. Solve the integrals of the functions: x^2 * exp (2x) t^2 * sin(t) x ln(x) exp(3z) * cos(3z) ln(x) / x^2 t * [ln(t)]^2 x^3 * sqrt (1-x^2) sin[ln(t)] ln(1+x^2) x^2 * cos (4x).

### Integrals with substitutions

See attachment Evaluate the given integral. First make a substitution that transforms it into a standard form using the given formulas. If a computer algebra system is available, compare and reconcile (if necessary) the result found using the integral table formula with a machine result.

### Integrating Technology in Math Classroom

Explain the importance of appropriately integrating Texas Instruments' CBL 2 (Calculator Based Laboratory), CBR 2 (Calculator Based Ranger), Fathom, a powerful data analysis software tool from Key Curriculum Press, and Excel into the middle school or high school mathematics classroom curriculum. Describe the benefits of their us

### Arc length and surface area..

Set up and simplify the integral that gives the length of the given smooth arc. Do not evaluate the integral. See attachment for problems

### Integrals and Derivatives

15. A) B) C) D) None of the above 16. What are the values of C0 and C1 in d(t) = C1 + C0t - 16t2, if d(1) = 4 and v(2) = -65? A) C0 = -1, C1 = 21 B) C0 = 1, C1 = -21 C) C0 = -1, C1 = 19 D) C0 = 0, C1 = 1 17. What does du equal in &#8747;2x(x2 + 1)5 dx? A) 2x B) 2u du C) 2x dx D) 5u4 18. What is

### Derivatives and Integrals

1. Let's say that f ''(k) = 0 @(13, -2). What does this mean? A) There is definitely an inflection point at that location. B) There might be an inflection point at that location. C) There definitely is not an inflection point at that location. D) There's no way to tell without first knowing what the specific function is.

### Calculus Problems

See the attachment Solve the initial problems. Express the given limit as a definite integral over the indicated interval [a, b]. Assume that [&#65532;] denotes the i th subinterval of a subdivision of [a, b] into n subintervals, all with the same lengths &#65532;x = (b - a) / n, and that &#65532; is the midpoint of th

### Two Dimensional Wave Equation

I have posted a 2-D Wave Equation problem with three free ends and one fixed end on the bottom. The question has parts a-e. I also posted notes on how to solve a 2-D wave equation problem along with the formulas used. Please refer to these notes so the terminology used will be the same for the solution that I need for this probl

### evaluate the integral..

I just uploaded a pdf that may help. Also please explain in detail how to get the limits since I have 2 other similar problems. Thank you all very much!! So far I have: If we set Z=1/X, then F(z)=P[Z<=z]=P[1/X<=z]=the integral of f(x) and f(x)=(1/pi)(1/(1+x^2)) The problem is I can't seem to figure out the

### Integers and Rational Numbers

1)For any integer a, argue that a + 3 > a + 2 3) An integer a is divisible by an integer b means there is an integer z such that a = b x z. use any properties of the integers through page 14 to prove that fir integers a,b and c such that if a is divisible by b and b is divisible by c the a is divisible by c. 4) let Z deno

### Integration by Substitution using Chain Rule

WEEK 8 PARTICIPATION QUESTIONS... 1) Integration by substitution comes from Chain rule. Integration by parts is a consequence Product Rule of Derivatives. Prove that... [f(x) g(x)]' = f(x) g' (x) + f(x) g(x) Take the integral with respect to x of both sides of the equation, what will happen? 2) Retirement annuity.