1. Solve for the area between x^3 − 6x^2 + 8x − y = 0 and...

1. Solve for the area between x^3 − 6x^2 + 8x − y = 0 and the x − axis.

2. Solve for the area bounded by y^2 + x − 4 = 0 and the y − axis.

3. Solve for the area of the arch of the cycloid x = θ − sinθ, y = 1 − cosθ.

4. Solve for the area bounded by x^2 − 2x − y = 0 and x^2 − 6x + y = 0.

Expert Solution

Ally Wells answered 2 years ago

Find the area of the region. 1) y=6x^2 and y= 8x-2x^2 2) y=1/2sin(pi x/6) and y=1/6x...

Find the area of the region. 1) y=6x^2 and y= 8x-2x^2 2) y=1/2sin(pi x/6) and y=1/6x 3) y=x^3-4x and y=5x

find the area bounded by x^2 − 6x + y = 0 and: a.) x^2 −...

find the area bounded by x^2 − 6x + y = 0 and: a.) x^2 − 2x – y = 0 b.) y=x c.) x^2− 2x − y = 0, and the x-axis. USING ITERATED INTEGRALS

A) Solve the initial value problem: 8x−4y√(x^2+1) * dy/dx=0 y(0)=−8 y(x)= B) Find the function y=y(x) (for...

A) Solve the initial value problem: 8x−4y√(x^2+1) * dy/dx=0 y(0)=−8 y(x)= B) Find the function y=y(x) (for x>0 ) which satisfies the separable differential equation dy/dx=(10+16x)/xy^2 ; x>0 with the initial condition y(1)=2 y= C) Find the solution to the differential equation dy/dt=0.2(y−150) if y=30 when t=0 y=

Solve (1+e^x)dy/dx+(e^x)y=3x^2+1 Solve (x^3+y^3)dx+3xy^2 dy = 0 Solve (y-cos y)dx + (xsiny+x)dy = 0 Solve (1+ln...

Solve (1+e^x)dy/dx+(e^x)y=3x^2+1 Solve (x^3+y^3)dx+3xy^2 dy = 0 Solve (y-cos y)dx + (xsiny+x)dy = 0 Solve (1+ln x +y/x)dx = (1-lnx)dy Solve (y^2+yx)dx - x^2dy =0 Solve (x^2+2y^2)dx = xydy Solve Bernoulli's Equation x dy/dx + 2y = (x^4)(e^x)(y^2) Solve Bernoulli's Equation (1+x^2) dy/dx = 2xy +(e^x)(y^2) Solve IVP (3e^(x^2))dy + (xy^2)dx=0 ; y(1) = 2 Solve IVP dy/dx -2xy = e^(x^2) ; y(0)=0 Solve IVP (x^2+y^2)dx+(2xy)dy=0; y(1)=1 6. Mixture Problem Initially 40 lb of salt is dissolved in a large...

a) Select all solutions of (d^2/dx^2)y(x)+64y(x)=0. y(x)=3cos(8x) y(x)=3cos(4x) y(x)=C1sin(8x)+C2cos(8x) y(x)=−4sin(8x) y(x)=C2cos(8x) b) Select all solutions of...

a) Select all solutions of (d^2/dx^2)y(x)+64y(x)=0. y(x)=3cos(8x) y(x)=3cos(4x) y(x)=C1sin(8x)+C2cos(8x) y(x)=−4sin(8x) y(x)=C2cos(8x) b) Select all solutions of (d^2/dx^2)y(x)+36y(x)=0. y(x)=C2cos(3x) y(x)=C1sin(3x) y(x)=3cos(3x) y(x)=3cos(6x) y(x)=3sin(3x)+8cos(3x)

solve y' +(x+2/x)y =(e^x)/x^2 ; y(1)=0

Consider the second-order boundary value problem y′′ +(2x^2 +3)y′ −y =6x, 0≤x ≤1, (4) y(0) =...

Consider the second-order boundary value problem y′′ +(2x^2 +3)y′ −y =6x, 0≤x ≤1, (4) y(0) = 1, y(1) = 0. (a) Rewrite the second-order equation (4) as a system of two first-order equations involving variables y and z. [2] (b) Suppose that yn and zn are approximations to y(xn) and z(xn), respectively, where xn = nh, n = 0,...,N and h = 1/N for some positive integer N. Find the iterative formula when using the modified Euler method to approximate...

Solve x′=x−8y, y′=x−3y, x(0)=2, y(0)=1

Solve the initial value problem: y'' + y = cos(x) y(0) = 2 y'(0) = -3...

Solve the initial value problem: y'' + y = cos(x) y(0) = 2 y'(0) = -3 y' being the first derivative of y(x), y'' being the second derivative, etc.

Let R(x) = ( 2x^2 − 8x + 6 ) / (x^2 + 6x + 8)...

Let R(x) = ( 2x^2 − 8x + 6 ) / (x^2 + 6x + 8) a) Find all x such that R(x) is undefined. Find all x such that R(x) = 0. Evaluate R(0). Graph R(x) indicating all vertical and horizontal asymptotes and x and y intercepts. b) Find the intervals on which ( x^2 + 2x + 12 ) / (x − 2) ≥ 2x + 5.

Question