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Integrals

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.

Line integral

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

Ellipse integral

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

How do you calculate the area enclosed between curves?

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:

What is the area enclosed between the two curves?

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

Computing for the Integral

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

Polynomial equations and integrating area under curve

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

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.

Inverse trigonometric functions, L'Hopitals Rule and Integration by Parts

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

Area between graphs

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.

An example using Cauchy's theorem

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.

Trigonometry: Solving Integrals

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.

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

Solve: Integration by 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.

Integration

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