### Integral test of series

Determine whether the series is convergent or divergent. 1 + 1/(2*sqrt[2]) + 1/(3*sqrt[3]) + 1/(4*sqrt[4]) + 1/(5*sqrt[5]) + ... Please show steps.

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Determine whether the series is convergent or divergent. 1 + 1/(2*sqrt[2]) + 1/(3*sqrt[3]) + 1/(4*sqrt[4]) + 1/(5*sqrt[5]) + ... Please show steps.

Pleas see the attached page for problems. Evaluate the line integral, where C is the given curve

See attached page for problem. Use the given transformation to evaluate the integral.

Please see the attached file for the three problems. Question 16: Give the are of the region bounded by the graphs of R(x) = -x^2 + 6 G(x) = x and the vertical line x = 3. Question 17: Give the area of the region bounded by the graphs of R(x) = -x^2 + 3 G(x) = -2x and the vertical line x = -2. Question 18:

Please see the attached file for three problems on area enclosed between curves. Question 13: Give the area of the region bounded by the graphs of G(x) = x^2 - 8 F(x) = 2x and the vertical line x = -3. Question 14: Give the area of the region bounded by the graphs of H(x) = x^2 - 10 Q(x) = 3x and the ver

Compute the following: 1. Integral(pi - 0) (-2cos (x) - 2sin (x)) dx a. -5 b. -4 c. -2 d. -6 e. 4 f. None of the above. 2. Integral(1 - 0) (-x + 3)^2 dx a. (16/3) b. (41/6) c. (35/6) d. (22/3) e. (19/3) f. None of the above. 3. Integral((1/6)pi - 0) (-cos (3x) dx) a. 1/6 b. -1/3 c. 2/3 d. -5/6 e

Let f be continuous on the interval [0, b]. Show that int( f(x) / (f(x) + f(b-x)), x=0..b ) = b/2 .

Show that if f is continuous on the entire real line then, Int(f(x+h)dx, x=a..b) = Int(f(x)dx, x=a+h..b+h).

I need to find the area of each with respect to the x axis I have the following 2 polynomial equations: (1) y = -24.034x^4 + 440.02x^3 - 2814.5x^2 + 7050.2x - 4660 y values range from 0 to 1275 and x values range from 0 to 6 (2) y = -721.34x^5 + 15484x^4 - 123523x^3 + 443283x^2 - 678627x + 396008 y values range fr

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

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.

Please see the attached file for the fully formatted problems. 1. Prove that d/dx (csc^-1 x) = - (1 / x(square root x^2 - 1) 2. Find the derivative of the function. Simplify where possible. y = tan^-1 (x/Q) + ln (square root (x-Q)/(x+Q)) 3. Find the limit using l'Hopital's Rule where appropriate. If there is a more e

For the functions: f(x)=4-x^2 g(x)=e^(-x) a. Sketch both graphs. Find and label the intersection points. b. Find the area between the graphs using integration. Give the full integral, including limits, in proper notation.

Let f be analytic on │z│> 1. Show that if r > 1, then the integral of f over C(0,r) is independent of r.

Let f be entire. Evaluate the integral from zero to 2 pi of f(z_0+re^(i theta)) e^(ik theta), where z_0 is a constant and k is a constant greater than or equal to 1.

Please see the attached file for the fully formatted problem.

Determine the integral 2xe^5xdx

7) Determine the integral (square root of 9x^2 + 4) /x^4 dx

Please solve the following integral: 1) Determine the integral sin^3(3x)cos^6(3x)dx Make sure to show all of the steps which are required.

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

3A)Determine the integral 2xe^-5x^2 dx by u substitution.

It is essential to show all steps by hand. Also if a method is prescribed, use only that method. Keeping this involved, solve the following: 1A) Determine the integral dx/x^2+12x+36 by using substitution. 1B) Determine the integral dx/x^2+12x+40.

Evaluate the given integrals by changing to polar coordinates. See attached page for the problems.

Please see the attached file for the fully formatted problems.

Evaluate the iterated integrals in the attachment.

Calculate the double integral. See attached page for the problems.

1) Int. Sinx dx. = ( Pi/2 to 3/2pi) ie definite integral of sinx with lower limit pi/2 and upper limit 3/2 pi

Integrate from 0 to 1 [(x^2 +1)e^(-x)]dx

Integrate [(e^(2t)/(1+e^(4t))]dt Thank you in advance for your time and effort!

(Integrate from 0 to 1) [(x^2+1)e^(-x)]dx Please show steps.