### Evaluating an integral in terms of areas

"Evaluate the integral by interpreting it in terms of areas: the integral as 0 goes to 8 of |5x-10|dx"

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"Evaluate the integral by interpreting it in terms of areas: the integral as 0 goes to 8 of |5x-10|dx"

Use the definition of integrals to evaluate the following integral: the integral as 1 goes to 8 of (2+3x-x^2)dx

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].

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

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

∫x/[x + (x^1/2) -2]

Please assist me with the attached problems, including: Show that the improper integral converges and find its value or show that it diverges ... Please see attachment for complete list of questions. Thanks

Please assist me with the 30 attached problems, including: - Finding integral - Finding exact value - Finding volume - Finding length

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 the mass of the rectangular prism .... with density function ... where m = triple integral of density. Please see the attached file for the fully formatted problem.

Use the attached function to derive the pair of integration functions {see attached for functions and diagram}

Use residues to evaluate the improper integrals (see the attachment to view the problem).

Evaluate the following integrals: 4 1. ∫ (2x-3)(x+2)dx 2 2 2. ∫ (2x+1)4dx 1 0.001 3. ∫ 50cos50πt dt -0.001 π/2 4. ∫ 5sin(2t-(π/6)dt 0

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.

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!}

Please solve the following problems: 1. Compute the following ... 2. Let Fm be the set of all integral multiples of the integer m. Prove that ... 3. Draw the graphs of the straight lines defined by the following Diophantine equations ... 4. Prove that every integer is uniquely representable as the product of a non-negati

Real Analysis Divergence Theorem Green's theorem stokes' theorem

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

Find the work done by a force F with F = (x,y,z) = (sinx, x+y, e^z) which results in the movement of a body along the curve C with parameterization r = (t, t^2, logt)for tE[1,2]. (See attachment for second question)

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)

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)

∫ (from 0 to Infinity)(3(theta)^3*(x)^2)/((x+ theta)^4) dx

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.

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.

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.

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.

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.

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.

Please see the attached file for full problem description.