1.Evaluate the integral C where C is x=t^3 and y=t, 0 ≤ t ≤ 1 2.Find...

1.Evaluate the integral C where C is x=t^3 and y=t, 0 ≤ t ≤ 1
2.Find the area of the surface with vectorial equation r(u,v)=<u,u sinv, cu >, 0 ≤ u ≤ h, 0≤ v ≤ 2pi

Expert Solution

If you have any doubts in the solution please ask me in comments ...

Here many concept are used which i written in summary before solution in second question please read carefully i solved it step by step please ask if you have any doubts

Colby Messinger answered 1 year ago

1A) Use surface integral to evaluate the flux of F(x,y,z) =<x^3,y^3,z^3> across the cylinder x^2+y^2=1, 0<=z<=2...

1A) Use surface integral to evaluate the flux of F(x,y,z) =<x^3,y^3,z^3> across the cylinder x^2+y^2=1, 0<=z<=2 1B) Use the Divergence Theorem to evaluate the flux of F(x,y,z) =<x^3,y^3,z^3> across the cylinder x^2+y^2=1, 0<=z<=2

Solve the following differential equations: 1. x"(t)+ x(t)=6sin(2t) ; x(0)=3, x'(0)=1 2.y"(t)- y(t)=4cos(t) ; y(0)+0 ,...

Solve the following differential equations: 1. x"(t)+ x(t)=6sin(2t) ; x(0)=3, x'(0)=1 2.y"(t)- y(t)=4cos(t) ; y(0)+0 , y'(0)=1

Let f(x,y)= (3/2)(x^2+y^2 ) in 0≤x≤1, 0≤y≤1. (a) Find V(X) (b) Find V(Y)

Let X = [1, 0, 2, 0]tand Y = [1, −1, 0, 2]t. (a) Find a...

Let X = [1, 0, 2, 0]tand Y = [1, −1, 0, 2]t. (a) Find a system of two equations in four unknowns whose solution set is spanned by X and Y. (b) Find a system of three equations in four unknowns whose solution set is spanned by X and Y. (c) Find a system of four equations in four unknowns that has the set of vectors of the form Z + aX + bY as its general solution where...

using / for integral Evaluate the double integral //R cos( (y-x)/(y+x) )dA where R is the...

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Solve the initial value problem: Y''-4y'+4y=f(t) y(0)=-2, y'(0)=1 where f(t) { t if 0<=t<3 , t+2...

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y''(t)+(x+y)^2y(t)=sin(xt+yt)-sin(xt-y*t), y(0)=0, y'(0)=0, x and y are real numbers

y''(t)+(x+y)^2*y(t)=sin(x*t+y*t)-sin(x*t-y*t), y(0)=0, y'(0)=0, x and y are real numbers

Solve the following differential equations: 1.) y"(x)+ y(x)=4e^x ; y(0)=0, y'(0)=0 2.) x"(t)+3x'(t)+2x(t)=4t^2 ; x(0)=0, x'(0)=0

Evaluate the integral from (1,pi/2,0) t0 (2,pi,0) of (2xsiny +x) dx +(x^2 cosy + 3sin^3(y)) dy...

Evaluate the integral from (1,pi/2,0) t0 (2,pi,0) of (2xsiny +x) dx +(x^2 cosy + 3sin^3(y)) dy giving the potential function

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