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Integrals

Brownian motion and Ito's formula

Hi, I've attached 2 questions in one file. Thanks. Question 1 hints: Hint 1: you have a process Y and a function, the first instinct should be to try Ito. Hint 2: what would the SDE of a martingale look like? Look at attached lecture note. Question 2 hint: Hint: use the integral version of Ito's formula.

Area using integration

Please show in detail how to solve the following area problem. Thank you. Let R be the region bounded by the graphs of f(x) = 4 - x^2/4 +8x Y =2, x-axis, y = -3

Reimann Sum

1. Write a Reimann sum and then a definite integral representing the volume of the region, uisng the slice show. Evaluate the integral exactly. ... 2. Find the volume of a sphere of radius r by slicing. ... [See attachment for questions.]

Work Done by Vector Field Along Helix and Straight Line

#4 in attached problem set (see attachment). 4. Find the work done by the force field F(x, y, z) = -zi + yj + xk in moving a particle from the point (3, 0, 0) to the point (0, pi/2, 3) along: (a) a straight line (b) the helix x = 3cos(t), y = t, z = 3sin(t).

Find the mass of the tetrahedron with vertices

Find the mass of the tetrahedron with vertices (0,0,0), (0,1,0), (3,0,0), and (0,1,4) with density f(x,y)= xy using iterated integral the instructor said that the integral needs to be divided into 2 integrals

Indefinite integral

Please show in detail how to solve the following indefinite integral. Thank you.

Indefinite integral

Please show in detail how to solve the following indefinite integral. Thank you. ∫sin^3(x)cos^19(x)dx

Solving Indefinite Integrals

Please show in detail how to solve the following indefinite integral. integral (x^2/(sqrt(16-x^2))dx Please see attachment for proper formatting.

Integrated integral for volume of a unit cube

Give an iterated integral describing the volume of a unit cube (side length 1) in cylindrical and spherical coordinates.. I just need the integral and a short explanation, I do not need them solved.

Differentiation and integration

See attached file for full description 1. Express the distance between the point (3, 0) and the point P(x, y) of the parabola y = x^2 as a function of x. 2. Find a function f(x) = x^k and a function g such that f(g(x)) = h(x) = sqrt(3x +x^2). 3. Find the trigonometric limit: lim(x->0) (x - tan2x)/sin2x 4. Given f(x)

Integrals

Improper Integrals of Certain Functions over (- infinity, infinity) Please check attached file. Please provide the detailed explanation.

Polynomial division and integration

Please show all steps Thank you 1) Divide 2x6 - x4 -3x2 + 7 by (x - 2). What is the sum of the remainder and the x^4 coefficient of the result? 2) Integrate: 2x(x2 + 3)4dx

Integral and series

7. Calculate per series the integral a  1. Is the result extendible to the values of a < 1? Justify.

application of triple and double integrals

See the attached file for full description. 26. Evaluate the triple integral, where E is bounded by the planes y = 0, z = 0, x + y = 2 and the cylinder y^2 + z^2 =1 in the first octant. Find the volume of the given solid 30. Under the surface z = x^2y and above triangle in the xy-plane with vertices (1, 0), (2, 1), and (4

Integrals

See attached Evaluate the following integrals...

Volume of solid, triple integral, sperical coordinates

Use spherical coordinates (iterated triple integral) to find the volume of the solid in the first octant whose shape is determined by the graph of the cone z=sqrt(x^2+y^2), the cylinder x^2+y^2=1 and the coordinate planes. NOTE: Please see attachment for original problem (question #4)and work i have done on it so far.