Chemical Engineering Answers

State Green s theorem and verify for ∮c(x²+y²)dx+(3y+2x)dy ,where C is triangle with vertices at (0,0),(1,0),(1,1)

Evaluate the line integral of →{v}=xyi+y^{2}zj+e^{2z}k over the curve C whose parametric representation is given by x=t^{2},y=2t,z=t,0<t<1.

Show that the vector →{v}=(yz-1)i-z(1+x+z)j+y(1+x+2z)k is conservative and find it scalar potential function.

Evaluate ∬R(x-y)^{2}sin^{2}(x+y)d xdy, where R is the rhombus withsuccessive vertices at (π,0),(2π,π),(π,2t) and (0,π)

Evaluate ∫y=0^{1}∫x=y^{2√2-y^{2}}y/2√x^{2}+y^{2}dxdy ,by clange the order of integration.

Solve dy/dx= 4x² (y-x)² + if y /x is a particular solution.

Solve (2y³xe^y+ y² + y)dx + (y³x²e^y-xy- 2x)dy = 0.

Find the equation of the family of all erhogonal trajectories of the family ofcircles which pass through origin and hav centres on the y-axis.

State Newton s law of cooling. If the temperature of the air is 30^{0}C and thetemperature of the body drops from 80°C to 60^{0}C in 10 minutes. What will beits temperature after 20 minutes.

Solve (x^{2}D^{2}+4xD+2)y=(logx/x)^{2},x>0 , where D=d/dx