Evaluate int_C (x + sqrt(y) ) where C is the concatenation of two curves C_1 and […]

# Calculus III

Show that the given line integral is independent of path, then calculate the value of the […]

## Show that the given line integral is independent of path, ...

F(x, y, z) = x^2z^2i + y^2z^2j + xyzk. S is the part of the paraboloid […]

## F(x, y, z) = x^2z^2i + y^2z^2j + xyzk. S ...

F(x, y, z) = xye^zi + xy^2z^3j - ye^zk. S is the surface of the box […]

## F(x, y, z) = xye^zi + xy^2z^3j - ye^zk. S ...

Compute the divergence and curl of the following vector fields F = sin( yz )i + […]

## Compute the divergence and curl of the following vector fields ...

Evaluate the parameterization of the line integral curve

## Evaluate the parameterization of the line integral curve

Integrate sqrt(1 + x^2) / x dx using trig substitution and then fully simplify.

## Integrate sqrt(1 + x^2) / x dx using trig substitution ...

Find the value of t so that the point (2, 2, t) is on the tangent […]

## Find the value of t so that the point (2, ...

Let S be the surface z = xy^2 + x^2e^(y-2). Find an equation of the form […]

## Let S be the surface z = xy^2 + x^2e^(y-2). ...

Let C be the curve in space parametrized by r(t) = (t, t^2, t^3). Find a […]

## Let C be the curve in space parametrized by r(t) ...

Let D be the region in the xy plane bounded by y=0, y=x^2, and x=1. Calculate […]

## Let D be the region in the xy plane bounded ...

Let F be the vector field F(x, y, z) = x^2i + yzj + xe^(3z)k. (a) […]

## Let F be the vector field F(x, y, z) = ...

int_C y dx + (x + y^2) dy if C is the ellipse 4x^2 + 9y^2 […]

## int_C y dx + (x + y^2) dy if C ...

int_C (x^2 + y^2 + z^2) ds if C is the curve r(t) - , 0

## int_C (x^2 + y^2 + z^2) ds if C is ...

Int_C F dot dr, where F = < ( 1 + xy ) e^(xy), x^2e^(xy) > […]

## Int_C F dot dr, where F = < ( 1 ...

Line integral ( y + e^sqrt(x) ) dx + (2x + cos(y^2) ) dy, where C […]

## Line integral ( y + e^sqrt(x) ) dx + (2x ...

Surface integral F = < x + yz, 2yz, x-y> and C is the intersection of […]

## Surface integral F = < x + yz, 2yz, x-y> ...

Let C be given parametrically by r(t) = , t : 0 to 1; the value […]

## Let C be given parametrically by r(t) = <1,-t^2,t>, t ...

Let S be the surface given by the graph of z=1-x^2-y^2, z>=0 and oriented so that […]

## Let S be the surface given by the graph of ...

Let C be given parametrically by r(t)=< t , e^(t^2) , e^t >, t : 0 […]

## Let C be given parametrically by r(t)=< t , e^(t^2) ...

Integrate (y + e^sqrt(x)) dx + (2x + cos(y^2)) dy, where C is the positively oriented […]

## Integrate (y + e^sqrt(x)) dx + (2x + cos(y^2)) dy, ...

Integrate the vector field F(x,y)=(-yi+xj)/(x^2+y^2) one time around the circle x^2+y^2=R^2 counterclockwise.

## Integrate the vector field F(x,y)=(-yi+xj)/(x^2+y^2) one time around the circle ...

Let F be a constant force field. Show that F does no work on a path […]

## Let F be a constant force field. Show that F ...

Evaluate integral F dot dr where C has parametrization r(t)=cos

## Evaluate integral F dot dr where C has parametrization r(t)=cos

PART 1 PART 2

## How to Sketch Sums and Difference of Vectors

PART 1 PART 2 PART 3