Area of a surface of revolution

NOTE: we are supposed to use the definition of the Area of a Surface of Revolution to solve this problem. I have attached this formula in a word document. The problem: Given: y = -x^2 + 4x defined on the closed domain [0,4] Revolve the graph about the x-axis. Find the area of the surface obtained.

center of mass for a plane region

I need to see how to find the centroid coordinates by using integrals and moments. I have attached the formulas to use and the answers I received in a word document. The answer I keep getting is (0,4.79) Here is the problem: Given: y = 9 - x^2, y = 2 Find the coordinates of the centroid of the above plane region. Th ...continues

Surface of the area of revolution

We are supposed to use the definition of the Area of a Surface of Revolution to solve this problem. I have attached this formula and the answers I received in a word document. The problem: Given: y = -x^2 + 4x defined on the closed domain [0,4] Revolve the graph about the x-axis. Find the area of the surface obtained ...continues

How to write line equation knowing the points

Write an equation and sketch a graph of the line through the points (-4,-3) and 3,12)

Solving trigonometric identities.

Solve for x: a) sin(^2)x=cosx-1 b) sin2x=cosx c) sin2x=2sinx

Calculating the limits of a sequence.

Use two methods to calculate the limit of the following sequence. x(n)=1/n^3+2^2/n^3+...+n^2/n^3

Implicit differentiation: Logarithms

Given equation ln(y/x)=x^2y^2 Find dy/dx

Simplifying polynomial expressions.

How do I simplify: [(8x)/(3x-6)]x[(x2-4)/(2x+4)]

integrals - trigonometric subsitution

The integral is to be solved using trigonometric subsitution. I have attached a word document with the integral to solve and my work. I want to know if my answer is correct. If my answer is not correct, I want to know the correct answer and the steps to get it. Thanks.

trigonometric integrals involving powers

I used the product to sum identities rule since the integral involved cosines of different angles. I have attached a word document with the integral to solve and my work. I want to know if my answer is correct. If my answer is not correct, I want to know the correct answer and the steps to get it. Thanks.