Calculus II Practice (2)

2017-07-26 00:42:18 +0900 -
Calculus 2

Evaluate the integral.

Q1)

A1)


Q2)

A2)


Q3)

A3)

$$ \therefore \frac{1}{2}(e-1)^2


Change the Cartesian integral to an equivalent polar integral, and then evaluate.

Q4)

A4)

,


Q5)

A5)

,

,


Q6)

A6)

,


Use the given transformation to evaluate the integral.

Q21) ,

where is the parallelogram bounded by the lines , , ,

A21)

,

,

,


If r(t) is the position vector of a particle in the plane at time t, find the indicated vector.

Q24) Find the velocity vector.

A24)

Velocity Vector:

,


Q25) Find the acceleration vector.

A25)

Acceleration Vector:


The position vector of a particle is r(t). Find the requested vector.

Q26) The velocity at for

A26)


Q27) The acceleration at for

A27)


Find the unit tangent vector of the given curve.

Q28)

A28)


Q29)

A29)


Calculate the arc length of the indicated portion of the curve .

Q30) ,

A30)


Evaluate the line integral of along the curve C.

Q35) , ,

A35)


Q36) , ,

A36)


Evaluate the line integral along the curve C.

Q37) , is the straight-line segment , , from to

A37)


Apply Green’s Theorem to evaluate the integral.

Q41)

: The circle

A41)


Q42)

: The triangle bounded by , ,

A42)

,


Find the divergence of the field F.

Q43)

A43)

Divergence


Evaluate the surface integral of G over the surface S.

Q46) is the plane above the rectangle and ;

A46)