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Integrals

Question Regarding Polynomials

(See attached file for full problem description with proper symbols). --- Let and for (a) Use integration by parts to show that in for . Deduce that for (b) Compute for and verify that.

Measurable Spaces and Properties of Integrals of Simple Functions

1).If A is a subset of B, A,B in m ( measurable sets) then show that integral (region A) s dM =< integral ( region B) s dM Where s here is a simple non-negative measurable function. ( Please don't confuse this with bounded measurable functions, I need the proof for SIMPLE functions). 2). If E are measurable, X_E is the c

Integration: Profit Function, Pesent Values and Future Values

An oil company discovered an oil reserve of 100 million barrels. For time t>0, in years, the company's extraction plan is a linear declining function of time as follows: q(t)=a-bt Where q(t) is the rate of extraction of oil in millions of barrels per year a time t and b= 0.1 and a =10 . a) How long does it take to exhaust

Area Bounded by Curves & Volume of Solid of Revolution

Find the area of each polar region enclosed by f(theta) for a <=theta<=b 36) f(theta) = theta/pi, 0<=theta<=2pi PLEASE SHOW EVERY STEP IN SOLVING THESE-NO COMPUTER PROGRAMS PLEASE. 4) Identify each curve as cardiode, rose(state # of petals), leminscate, limacon, circle, line or none of above. a) r=2sin2theta b) r^2=2c

Using Integrals to Find the Area Bounded Between Curves

Sketch the region bounded between the given curves and then find the area of each region for 16 and 22. 16) y=x^2+3x-5, y=-x^2+x+7 22) x axis, y=x^3-2x^2 -x+2 28) Find the area of the region that contains the origin and is bounded by the lines 2y=11-x and y=7x+13 and the curve y=x^2-5. Please see the attached file f

Integrals Application Word problem : Supply and Demand Curves and Equilibrium

4. The demand curve for a product has equation p=20 e^(-0.002q) and the supply curve has equation p=0.02q + 1, where q is the quantity and p is the price in $/unit. a) Which is higher the price at which 300 units are supplied or the price at which 300 units are demanded? Find both prices. b) Sketch the supply and deman

Definite Integrals : Supply and Demand Curves and Equilibrium

6. The demand curve for a product has equation p = 100 e^(-0.008q) and the supply curve has equation p = (4&#8730;q) + 10 , where q is the quantity and p is the price in dollars/unit. a) At a price of $50, what quantity are consumers willing to buy and what quantity are producers willing to supply? Will the market push price

Definite Integrals Application Word Problem : f(t) = 100e^(-0.5t)

A service station orders a 100 cases of motor oil every 6 months. The number of cases of oil remaining t months after the order arrives is modeled by f(t) = 100e^(-0.5t) a) How many cases are there at the start of the six-month period? How many cases are left after the end of the six-month period? b) Find the average number

Integrals Trigonometric Functions

Evalutate the following: 1.) Integrate sech ^2x/ (2+ tanh x) dx 2.) Integrate from 0 to (Pi/2) sinx/(1+cos^2 x) dx 3.) Find (f^-1)' (a) of f(x)=x^5 - x^3+ 2x, a=2 4.) Find the limit x approaches (2-) e^(3/(2-x))

Convolution integral method

Use the convolution integral method and hand calculation to come up with the exact formula for the solution of y'' [t] + 5y' [t] +6y[t]= 3.8E^(-t) with y [0]=2 y' [0]= -1

Graphing and TI-83 : Plotting a Graph an Calculating an Integral

I need help with the TI-83. I dont want the problem solved, just need to be walked through the steps for inputting data into the TI-83 to mimic the graph as shown in the document. I have tried many ways and I keep getting the wrong graph. Thank You. a) Graph x3 - 5x2 + 4x , marking x = 1,2,3,4,5 b) Use th

Integrals, Marginal Cost Function and Marginal Profit

The marginal cost function of producing q mountain bikes is a) If the fixed cost in producing the bicycles is $2000, find the total cost to produce 30 bicycles b) If the bikes are sold for $200 each, what is the profit (or loss) on the first 30 bicycles c) Find the marginal profit on the 31st bicycle. Please see the atta

Graphing and interpretation of definite integrals.

A) Graph , marking x = 1,2,3,4,5 b) Use the graph and the area of interpretation of the definite integral to decide which of the five numbers for n = 1,2,3,4,5 is largest. Which is smallest? How many of the numbers are positive? (Do not calculate integrals). (See attached file for full problem description)

Vector calculus: Surface Integral, Moment of Inertia of a Lamina

#22) Find the moment of inertia of a lamina S of density 1 about an axis A, where S: x2+ y2=1, A: the line z= h/2 in the xz-plane (See attached file for full problem description with equations) --- Question in Kreyszig's Advanced engineering mathmatics 8th ed.: section 9.6: Surface integrals

Vector calculus: Surface Integrals

#16) Surface integrals; &#61682;s&#61682; G(r) dA. Evaluate these integrals for the given data. (show the details.) G=(x2+ y2)2 - z2, S: r=[u cos v, u sin v, 2u], 0&#61603; u &#61603;1, -&#61520; &#61603; v &#61603; &#61520; (See attached file for full problem description with equations) --- Kreyszig's Advanced e

Vector Calculus: Surface Integral

#12) Surface integrals; &#61682;s&#61682; G(r) dA. Evaluate these integrals for the given data. (show the details.) G=cosx + siny, S: the portion of x+y+z=1 in the first octant (See attached file for full problem description with equations) Question in Kreyszig's Advanced engineering mathmatics 8th ed.: section 9.

Line Integral and Complex Form of Green's Theorem

(See attached file for full problem description with equations and diagram) --- Compute &#8747;r+ (bar-z + z^2 bar-z) dz where gamma+ is a square with side = 4, centered at the origin and traced counterclockwise once ---

Continuity and Outer Measure

Let f(x) be a positive continuous function on [0,1/2], f(x) =< 1/2. Let A = { (x,y) : 0 =< x = 1/2, 0=<y=< f(x)} Prove that; m*(A) = integral from 0 to 1/2 of f(x)dx. Please I don't want a solution from a book, I want a simple proof based on basic definitionsand given info.

Integration : Finding Volume of a Disc

Find the volume of y = 1/sqrt(1+x^2) bounded by y=0, x=-1, x=1 I'm using the disc method with a dx function: V = pi integral( [R(x)]^2 ) dx Therefore, I have V = pi integral( [1/sqrt(1+x^2)] ^2 ) dx from -1 to 1 = pi integral( [ 1/(1+x^2) ] ) dx from -1 to 1 I can't figure out how to integrate. Please explai

Integration: Find the Arc Length Over an Interval

Find the arc length of the graph of the function over the indicated interval: y=1/6 x^3 + 1/(2x^2), [1,3] I know S = Intergral( sqr( 1 + [f'(x)]^2 )) dx from 1 to 3. I get y' = [ 1/9 x^4 - 1/3 + 1/(4x^4) ] dx Therefore, S = Intergal( sqr( 1 + 1/9 x^4 - 1/3 + 1/(4x^4) )) dx from 1 to 3 = Intergal( sqr( 2/3 + 1

Normed Space, Compactness and Transformation

Let X be a normed space, I closed interval ( or half-open on the right) and a = inf I, b = sup I. Let h : I -> [0,infinity) be a continuous function such that integral ( from a to b ) h(t)dt < positive infinity where integral from a to b represents the improper integral when I is not closed. Let epsilon > 0 and

Volumes of solids

Use shells to find the volume of the solid formed by revolving the given region about the y-axis. 22) the region bounded by the curve y=SQRT(x), the y-axis, and the line y=1. 24) the region bounded by the parabolas y=x^2, y=1-x^2, and y axis for x&#8805;0. 26) the region inside the ellipse 2(x-3)^2 + 3(y-2)^2 = 6 about

Volumes of Solids: Washers and Disks

Find the volume of the solid formed when the region described is revolved about the x axis using washers and disks. 14) the region under the curve y= cubed root of x on the interval 0&#8804;x&#8804;8. 16) the region bounded by the lines x=0, x=1, y=x+1, and y=x+2. 20) the region bounded by the curves y=e^x and y=e^-x on