### Use series to approximate the definite integral I; Using multiplication or division of power series to find nonzero terms in Maclaurin Series

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

1) Evaluate. ∫ sinh^6 x cosh x dx 2) Evaluate. ∫ [ (√x+4)^3 / 3√x ] dx 3) Evaluate. ∫ x^2 sin(2x) dx 4) Evaluate. ∫ sin^5 x dx Please see attachment for actual sample problems.

3. Solve the wave equation, ∂2u/∂t2 = c2(∂2u/∂x) -∞ < x < ∞ With initial conditions, u(x,0) = (1/x2+1)sin(x), and ∂u/∂t(x,0) = x/(x2+1) 4. Suppose that f is a 2п-periodic differentiable function with Fouier coefficients a0, an and bn. Consider the Fourier coeffici

1. Evaluate: ∫2cos2 xdx 2. Figure 12.1 y = 9-x2 , y=5-3x Sketch the region bounded by the graphs of Figure 12.1, and then find its area. 3. Figure 13.1 1?0x4dx Approximate the integral (Figure 13.1); n=6, by: a) first applying Simpsonfs Rule and b) then applying the trapezoidal rule. 4. Find

LetR be the region bounded by the graph of f(x)=3x^2+6x and g(x)=18x-5x^2. 1) determine the area of R 2) Determine the volume of the solid of revolution formed when R is revolved about the line y=18. Please answer in detail.

Evaluate the integral. (integral from 0 to 1) dt/sqrt[16t^2+1] Use Hyperbolic inverse and show steps please!

Differentiate the function f(x) = ln(2x + 3). Find . lim e^ 2 x/(x+5)^3 →∞ Apply l'Hopital's rule as many times as necessary, verifying your results after each application. Evaluate ∫ x sinh(x)dx . Determine whether 2 ∫ (x / ^(4-x^2)) (dx)

Evaluate ∫3x+3 / x^3-1 (dx) Use trigonometric substitution to evaluate ∫1 / ^/¯1+x2(dx) Determine whether converges or diverges. If it converges, evaluate the integral. ∞∫-∞ 1 / 1+x2 (dx)

Evaluate ∫(^/¯x+4)^3 / 3^/¯x(dx) ∫x2sin2x dx ∫ sin5xdx

Evaluate: ∫ sinh6 xcosh xd x Given ?(x)= csch^-1 1 /x2 find ?'(x) Given ?(x)=log10x find ?'(x).

Find an upper and lower bound for the integral using the comparison properties of integrals. 1∫0 1 /x+2(dx) Apply the Fundamental Theorem of Calculus to find the derivative of: h(x)= x∫2 ^/¯u-1dx Evaluate: 4∫1 (4+^/¯x)^2 / 2^/¯x (dx) Evaluate: ∫2cos^2 xdx Sketch

Integrate...over the curve...in the first quadrant...from...

Integrate...over the the portion of the plane...that lies in the first octant. Please see the attached file for the fully formatted problems.

Show that if R is a region in the plane bounded by a piecewise smooth simple closed curve C then area is given by.... Please see the attached file for the fully formatted problem.

See attached word doc.

Evaluate a. b. c. d. An object is moving so that its velocity after t minutes is meters per minute. How far does the object travel from the end of minute 2 to the end of minute 3? a. 31 meters b. 61 meters c. -29 meters d. -9 meters

See attached word doc.

Given a spherical Bessel function J1(w) = (1/w^2)*(Sin(w)-w*Cos(w)) Show that (pi)*x/2, -1<x<1 integral of J1(w)*Sin(wx)dw from 0 to infinity = 0, |x|>1 Need a through explanation!!

1. Use the composite Trapezoidal Rule with indicated values of n=4 to approximate the following integrals See Attached file for integrals. 2. Use the Excel programs for Simpson's composite rule to evaluate integrals in Problem 1. 3. Use Gaussian Quadratures with n = 2, n = 4, n = 5 to evaluate integrals in Problem 1.

Please see attached file for full problem description.

? Find if . ? Find if and . ? A particle is moving with acceleration . Find the position function at time if and the velocity at zero, .

Please see the attached file for the fully formatted problems.

Please see the attached file for the fully formatted problems.

Please see attached file for full problem description. 1. What is the average value of the function f in Figure 6.4 over the interval ? From the graph, we can approximate: The average value of f on the interval from 1 to 6 is 3. Find the average value of over the interval [0, 2]. The average value

Please see attached file for full problem description. 16. An old rowboat has sprung a leak. Water is flowing into the boat at a rate given in the following table. t minutes 0 5 10 15 r(t), liters/min 12 20 24 16 (a) Compute upper and lower estimates for the volume of water that has flowed into the boat during the 1

I need some help to integrate the following W= I we( ^-rt) dt Where I is the Integral Upper Limit = T Lower Limit = S If you can work this out using the notation what would be helpful part 2: is it possible to take logs and solve for lnw