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# Integrals

### Integrate [ (1 + cos^2x)/(cos^2x)] from 0 to Pi/4

Integrate [ (1 + cos^2x)/(cos^2x)] evaluate from 0 to Pi/4

### 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.

### Integration question - Evaluate Int of sin^2 q dq

Evaluate Int of sin^2 q dq ... [See attached question file for equation.]

### 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.]

### Evaluate the integrals by parts twice to find functions

1. Write arctan ... 2. Evaluate the integrals ... 3.Use integration by parts twice to find ... [See the attached questions file.]

### 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.

### Integration Questions

Integration - [See attachment for equations.]

### Calculus - Differentiation Equations

Integraiton - (4) Ů e^-x dx ... [See attached file for equations.]

### 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 and limits

See attachment for equation

### Integrals

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

### Improper Integrals of Certain Functions over (- infinity, infinity)

Improper Integrals of Certain Functions over (- infinity, infinity) Please check attached file. Please provide the detailed explanation. Let f(z)=P(z)/Q(z) be a rational function where...

### Calculus - Antiderivatives & Integrals

Find antiderivatives and Integrals. ... [See the attached questions file.]

### Using integral to find the area between curves

1. true or false the area of the region by y=x, y=1/x, x=2 is 3/2-ln(2) 2. find the area of the region bounded by y=-x^2+6x y=-x+6

### 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

### Trigonometric integrals and binomial expansion

See attached Evaluate the integrals.... Show, using binomial expansion, that ....

### Integrals

See attached Evaluate the following integrals...

### Numerical Integration of a Differential Equation

Solve the attached differential equation by numerical integration.

### Integrate by using a substitution

Step by step detailed solution is provided to explain the concept of integration by substitution.

### Integral Problem: Prove the Sides Are Equal

Prove the sides are equal. See attachment.

See attached

### 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.