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Definite integral

Evaluate the definite integral, use a graphing utility to show your results: (see equation in attached file)

Finding the Volume of a Solid of Revolution

Problem: The region R is bounded by the graphs of x - 2y = 3 and x = y2. Find the integral that gives the volume of the solid obtained by rotating R around the line x = -1. I'm having a hard time setting up the integral, I think that I have the concept for finding the area of a 2d object using an integral but can't figure out

Finding Integrals (8 Problems)

(See attached file for full problem description with proper symbols) --- Answers and working for Integration questions: 1.Integrate the following functions with respect to . (i) sin(5 - 4) (ii) cos(3 - 2) 2. Integrate the following functions with respect to x. (i) 4e-3x (ii) (

Applications of Integrals : Velocity and Acceleration

Newton discovered that the falling acceleration of all objects in a vacuum, regardless of their sizes and weights, is the same. A raindrop falls down to earth with the same acceleration as a big metal ball drops from the edge of a building. He came up with the value of 9.8 meters per square second (s2) for the falling accelerati

Integration, limits, and curves

Note: x is used as a letter only not as a multiply sign 1. Find the volume of the solid generated by revolving the region enclosed by y= x^(1/2), y=0, x=4 about the line x=6. 2. Find the arc length of the graph of the function y = x^(3/2) - 1 over the interval [0,4] 3. Integrate ∫ [(Pi / 2) / 0] x cos x dx

Cartesian Coordinates, Convergence and Divergence

1. Find the equation of the tangent line in Cartesian coordinates of the curve given in polor coordinates by r = 3 - 2 cos Ø, at Ø= (π / 3) 2.Test for convergence or divergence, absolute or conditional. If the series converges and it is possible to find the sum, then do so. a) ∑[∞/n=1] (3/ 2^n)

Integrals : Finding Work Done

A 100 ft length of steel chain weighing 15 lb/ft is hanging from the top of a tall building. How much work is done in pulling all of the chain to the top of the building? keywords: integration, integrates, integrals, integrating, double, triple, multiple

Integrating factor

Solve for "c" (3y^2+2xy)dx-(2xy+x^2)dy =0 I see that the equation is not exact. differentiate the 1st side by My and the second by Nx. which gives me My=6y+2x and Nx= 2y+2x I add these togeter and divide by the "N" term and come up with an integrating factor of x^4. This still doesn't make the equation exact.


What are situations where knowing the exact definite integral is important as opposed to just knowing the indefinite integral?

Integration using trigonometric substitutions

I need help with these various integral problems if i need to use integration by parts, some substitution, trigonometric substitution, or partial fraction on these problems please show full step by step solution. See attached file for full problem description.

Graph : Finding the Area of a Shaded Region

(See attached file for full problem description with image) The graph below represents the function f(x) = x3 + 2x2 - 5x - 6. Explain how you process the calculation of the shaded region.


(See attached file for full problem description) integrate these problems: (make sure to show your work, don't just use math software)

Integration of exponential

Integration of exponential: I am having difficulty integrating exponential. I want to compute the indefinite integral of r`(t) where r`(t) is the vector <3, -e(^ -t), 0> The first integration I have is <3t+c1, ------- c3> I am not sure how to integrate the -e^-t ------------------------------------------

Real analysis - Step Functions and Riemann Integrals

If f is defined on [a,b] and and are, respectively, a nondecreasing and a nonincreasing sequence of step functions such that for all k and all and for almost all , show that f is Riemann integrable on [a,b]. Notes from section of book below: Section 5 Notes: Theorem 5.1 If f is Riemann integrable on [a,b],

Converting a double integral into a triple integral.

I have a double integral of the form I from 0 to 2 and I from 0 to y (4-y^2) dx dy How does one convert this double integral into a triple integral? keywords: integration, integrates, integrals, integrating, double, triple, multiple

Finding area under normal curve

Find the area under the normal curve which is shaded on the graph. Use 4 decimal places. See attached file for full problem description.

Integrals, Rate of Change and Recangle Inscribed in an Ellipse

(See attached file for full problem description) I need help with 7C, 10 and 12 7. Find the integral... 10. A beacon on a lighthouse 2000 m away from the nearest point P on a straight shoreline revolves at the rate of 10 pi radians per minute. How fast is the beam of the light moving along the shoreline when it is 500 m fro

Real Analysis : Integral Proof

If X(c,d) is the function from into such that X(c,d)(x)={1 if xE(c,d) and (c,d)&#8834;[a,b], show that &#8747;a-->b Xc,d =d-c. {0 otherwise Please see the attached file for the fully formatted problem.