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Integrals

Solve these 2 indefinate integrals

1) indefinite integral of dx / ((x^2)(sqrt[a^2-x^2])) with respects to x In words it is the integral of the derivative of x all over the quantity of x squared times the square root of a squared minus x squared 2) indefinite integral of dx / ((e^x)(sqrt[4+e^2x])) with respects to x in words it is the integral of the der

D-contour intervals

I need help on how to work out the solution to a function using the 'D-contour' (see attached file).

Polynomial

(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 Sets and 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

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

Differential equations...

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

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.

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 : 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