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Integrals

Integral of a Contour

Calculate the following integrals: ∫ from 0 to ∞ x^¼/(x²+9) dx Please see attached for proper format.

Residues and Closed Contours : Solve the Integral

Calculate the following integral... Please see attached for full question. Solution. Consider a close contour C shown above, where C consists of and a line segment from -R and R. Consider positive orientation, namely, clockwise. Choose r large enough so that are in the region covered by C. Let . By residual Theorem

Integral of Continuous Decreasing Function on a Closed Interval

Suppose f(x) is continuous and decreasing on the closed interval (4 is less than or equal to x is less than or equal to 11), that f(4)=6, f(11)=3, and that the integral as 4 goes to 11 of f(x)dx=27.01678. What is the integral as 3 goes to 6 of f^-1(x)dx?

Properties of Integrals : Verify an Inequality

Use the properties of integrals to verify the inequality without evaluating the integral: [the integral as 1 goes to 2 of (sqrt(5-x))dx] is greater than or equal to [the integral as 1 goes to 2 of (sqrt(x+1))dx].

Integrals : Riemann Sum with Diagrams

This question has me going around in circles. I can't make the Sigma symbol on the computer, so I used the word "Sigma" instead. For (c), n is above the Sigma symbol and i=1 is below it. (a)Find an approximation to the integral as 0 goes to 4 of (x^2-3x)dx using a Riemann sum with right endpoints and n=8. (b)Draw a diagram

Elementary Numerical Analysis

GAUSSIAN NUMERICAL INTEGRATION 1. Consider approximating integrals of the form... in which f(x) has several continuous derivatives on [0, 1] a. Find a formula... which is exact if f(x) is any linear polynomial. b. To find a formula... which is exact for all polynomial of degree ≤ 3, set up a system of four e

Integrals; Sine; Cosine; Bounded Region etc.

Please assist me with the attached problems. Examples: 2. Find each integral 5. Integrate equations using tables 6. Derive the sine squared formula 42. Use substituion to integrate certain powers of sine and cosine 52. Find the area of the region bounded by the graphs etc. (see attachment)

Arc Length of Curve, Tangent Line, Limits and Solid Revolution

1. Find the volume of the solid generated by revolving the region enclosed by: {see attachment} 2. Find the arc length of the graph of the curve {see attachment} 3 - 7. Integrate attached equations ... 8. Find the limit of the improper integral: {see attachment} 9. Find the arc length of the curve given in parametric

Integral

Find the integral of [x/(-x^2+6x+13)^(1/2)]dx

Residues and Poles : Cauchy Integral Formula

Find the value of the integral: {see attachment} taken counterclockwise around the circle (a) |z - 2| = 2 (b) |z| = 4 Please specify the terms that you use if necessary and clearly explain each step of your solution.

Volume of Solid of Revolution (4 Problems)

52. Find the volume V of the solid with the given information regarding its cross-section: {see attachment for info and diagram) 55. Find the volume of the solid generated when the region {see attachment} on the interval {see attachment} is revolved about a) the x-axis b) the y-axis c) the line y = -2

Find Areas and Sketch Bounded Regions (Curve)

2. Sketch a vertical or horizontal strip and find the area of the given regions bounded by specified curves: a), b), c) and d) {see attachment!} 3. Sketch the region bounded by and between the given curves and then find the area of each region: a), b), c), d), e) and f) {see attachment!}