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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)

Find Areas and Sketch Bounded Regions (Curve) (10 Problems)

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!}

Multiple Intergration, Area, Center of Mass, Moment, Centroid and Jacobian

1.Given the region R bounded by y=2x+2 , 2y=x and 4. a) Set up a double integral for finding the area of R. b) Set up a double integral to find the volume of the solid above R but below the surface f(x,y) 2+4x. c) Setup a triple integral to find the volume of the solid above R but below the surface f(x,y)=-x^2 +4x. d) Set

Evaluate the path integral of a helix.

Let C be the helix, with parameterization r(t)=(cost, sint, t), tE[0,2pi] and let f(x,y,z) = x^2 + y^2 + z^2. Evaluate the path integral. (See attachment for full question)

Integral of a Principal Branch

Show that the integration from -1 to 1 z^i dz = ((1+e^-pi)/2)*(1-i)where zi denotes the principal branch... (See attachment for full question)

Double Integral : Disc

By changing variables to polar coordinates evaluate the integral , where And , i.e., the disc of radius 3 centred at the origin. Please see the attached file for the fully formatted problems.

Double Integral : Change of Variables to Polar Coordinate

Prove ∫ 0 --->∞ e^(-x^2) dx = sqrt(pi)/2 Hint: multiply the integral with itself, use a different dummy variable y, say, for the second integral, write it as a double integral, and use change of variables to polar coordinate.

Euclid's Division Lemma and Fundamental Theorem of Arithmetic

1. Without assuming Theorem 2-1, prove that for each pair of integers j and k (k > 0), there exists some integer q for which j ? qk is positive. 2. The principle of mathematical induction is equivalent to the following statement, called the least-integer principle: Every non-empty set of positive integers has a least element.

Double Integral and Change of Order of Integration

I) Evaluate the integral.... ii) Change the order of integration and verify the answer is the same by evaluating the resulting integral. Please see the attached file for the fully formatted problems.

Analysis of a Midpoint of a Line Segment

Let C denote the line segment from z = i to z= 1. By observing that, of all the points on that line segment, the midpoint is the closest to the origin, show that |∫c dz/z^4| ≤ 4 sqrt(2) without evaluating the integral. Please see the attached file for the fully formatted problems.

Integral of a Semicircle and Segment

F(z) = z - 1 and C is the arc from z = 0 to z = 2 consisting of (a) the semicircle z = 1 - e^(iθ) (pi ≤ θ ≤ 2pi) (b) the segment 0 ≤ x ≤ 2 of the real axis. Find the integral ∫c f(z) dz for the two cases.