Integration
Integration of Exponential Functions. See attached file for full problem description.
Integration of Exponential Functions. See attached file for full problem description.
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4. A quantity of gas with an initial volume of 1 cubic foot and a pressure of 2500 pounds per square foot expands to a volume of 3 cubic feet. Find the work done by the gas for the given volume. Assume that the pressure is inversely proportional to the volume. 6. Find moment of mass M_x, M_y, and center of the mass for the la
#7,8 and 9 Please see attached file.
A 6.00 in radius cylindrical rod is 2 ft long. Use a differential to approximate how much nickel (in in^3) is needed to coat the entire rod with the thickness of .12 in. keywords: integrals, integration, integrate, integrated, integrating, double, triple, multiple
Evaluate the double integral integral from y=0 to y=3 of integral from x=0 tp 1-y of (x+y)dxdy int ( int (x+y), x=0..1-y), y=0..3)
The function K is defined as the following (attached). Please evaluate Ck and dk step by step.
There are three problems in one question. a) in polar coordinates, write equations for the line x=1 and the circle of radius 2 centered at the origin b) write an integral in polar coordinates representing the area of the region to the right of x=1 and inside the circle c) evaluate the integral
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Regions and Curves. See attached file for full problem description. Sample problems 1. ∫(e-2x)dx 2. Find area under curve, f(x)=(1/x²) on [1,2] 3. ∫18 5x(2/3)dx 4. ∫19 (√x+(1/√x))dx 5. ∫0√3 x(x²+1)(3/2)¬dx 6. ∫¬35 (3/(x-2))dx 7. Find the area of the region bounded by f(x)=ex, g(x)=(1/2
Prove that if f(x) is even on [-a, a] and integrable on [0, a] where a>0, then f(x) is integrable on [-a, a] and Int([-a, a], f(x)dx) = 2*Int([0, a], f(x)dx).
10. Stock Values. Integrated Potato Chips paid a $1 per share dividend yesterday. You expect the dividend to grow steadily at a rate of 4 percent per year. 1. What is the expected dividend in each of the next 3 years? 2. If the discount rate for the stock is 12 percent, at what price will the stock sell? 3. What is the exp
Find the surface integral (double integral over S) E dot dS, where S is the cylinder, x^2 + y^2 = 4, z is greater than or equal to 2 and less than or equal to 5, and the vector field F is F(x, y, z) = (0, 0, z^2)
Find the flux of the vector field F(x, y, z) = (y, 0, z2) out of the unit sphere S. In other words, find the surface integral ∫∫S (y, 0, z2) * dS, where the sphere S is oriented by the outward normal. Let S be the cylinder x2 + y2 = 1, 0 ≤ z ≤ 6. Find ∫∫S (x4 + 2x2y2 + y4)2 dS.
Let S be the conic surface z = 3 sqrt (x^2 + y^2), where z is greater than or equal to 0 and less than or equal to 3. Find (double integral over S) z dS.
Find the area of the region bounded by: (using integrals) a)F (x) = 6x- x^2 and g(x)= x^2 - 2x b) y = x^2 - 4x and y = x-4 keywords: integration, integrates, integrals, integrating, double, triple, multiple
The marginal revenue for a certain product is given by dR/dx = 25-2x. Find the change in revenue when sales increase from 7 to 10 units. keywords: integration, integrates, integrals, integrating, double, triple, multiple
Find y = f (x) if a) dy/dx = xe^(〖-x〗^2 ) and f(0) = 2 b) f"(x) = 1/e^x + 2 , f'(0) =3, f (0) = 1 keywords: integration, integrates, integrals, integrating, double, triple, multiple
Evaluate: a) ∫(〖 (2/x) + 3)〗^2 dx (using log) B) ∫_(-1)^2▒〖(2x-1)〗 dx C) ∫_0^1▒〖x√(1-x^2 )〗 dx Please show all work/steps.
Evaluate the double integral: / / l l (3x -2y)dA; R is the region enclosed by the circle l l x^(2) + y^(2) = 1 . / /
Let C be the curve represented by the equations x = 2 t , y = 3 t^(2). Evaluate the integral (0 <= t <= 1) / l (x - y)ds . l / C
Suppose m is a positive measure on X, m(X) < inf f is an element of L^(inf), ||f||_inf<inf and a_n= int (|f|^n)dm for n = 1,2,... where the integral is evaluated over the set X Show that lim as n->inf of (a_(n+1))/(a_n) is equal to ||f||_inf
Evaluate the iterated integral: / pi / x^(2) l l (1/x)cos(y/x)dydx l l / pi/2 / 0
Evaluate the iterated integral: / 1 / x^(2) l l (x^(2) - y) dy dx l l / -1 / -x^(2)
Find I = ∫c y2 dx + y dy, where c: x = cost, y = sint, 0 ≤ t ≤ pi. Evaluate the integral I = ∫c y dx + x dy, where the path c is given by x = t3 + 1, y = 1/(t3 + 1) and 0 ≤ t ≤ 1. keywords: integration, integrates, integrals, integrating, double, triple, multiple
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1. Show that the Cantor function c: [0, 1] → [0, 1] is continuous. To do this, I know I need to use the fact that c is monotone, but I'm having difficulty from there. 2. Compute ∫c, where c is considered to be an element of L+(R). (let c(x) =0 for x not in [0, 1]) Here, c is the Cantor Function and L+(R) consists
1) A plate is bounded by the curves y = 0, y = x^2 + 1, x = -1 and x = +1. It has density d(x,y) = x^2. Find its center of mass (x bar, y bar) 2) Find the length of the path c'. x = 1, y = t, z = t^2/2, t is greater than or equal to 0 and less than or equal to 1.
Use the Cauchy Integral Formula to show that where the unit circle is oriented counterclockwise, and use this fact to show that Please see the attached file for the fully formatted problems.
Let C be the boundary of the square of side length 4, centered at the origin, with sides parallel to the coordinate axes, and traversed counterclockwise. Evaluate each of the attached integrals.