Use Green's Theorem to evaluate the following line integral. Assume the curve is oriented counterclockwise The circulation line integral of Fequalsleft angle 4 xy squared comma 2 x cubed plus y right angle where C is the boundary of StartSet (x comma y ): 0 less than or equals y less than or equals sine x comma 0 less than or equals x less than or equals pi EndSet

The answer is

Step-by-step explanation:

Recall that green theorem is as follows: Given a field F(x,y) = (P(x,y),Q(x,y)) and a closed curve C that is counterclockwise oriented. If P and Q are continuosly differentiable, then

where R is the region enclosed by the curve C.

In this particular case, we have the following field . We are given the description of the region R as . So, in this case (calculations are omitted)

Thus,

So,

Since , then

Consider the integrals

Then, by using integration by parts (whose calculations are omitted) we get

Then, we have that

do you have a picture of the table

answer:   28.56 feet (approx)

step-by-step explanation:

since, triangle abc has measure of angle c equal to 55 degrees, measure of angle abc equal to 90 degrees, and length of bc equal to 20 feet.

we have to find out the measurement of segment ab.

therefore, tan 55° =

but bc = 20 feet.

⇒ tan 55 ° =  

⇒ ab = 20 × tan 55 °

⇒ ab = 20 × 1.42814800674

⇒ ab = 28.5629601348   ≈ 28.56 feet