Use the Fundamental Theorem of Line Integrals to calculate ∫c F⃗ ⋅dr⃗ exactly, if F⃗ =3x2/3i⃗ +ey/5j⃗ , and C is the quarter of the unit circle in the first quadrant, traced counterclockwise from (1,0) to (0,1). ∫c F⃗ ⋅dr⃗ =?

It looks like the vector field is

F(x, y) = 3x ^(2/3) i + e ^(y/5) j

Find a scalar function f such that grad f = F :

∂f/∂x = 3x ^(2/3)   =>   f(x, y) = 9/5 x ^(5/3) + g(y)

=>   ∂f/∂y = e ^(y/5) = dg/dy   =>   g(y) = 5e ^(y/5) + K

=>   f(x, y) = 9/5 x ^(5/3) + 5e ^(y/5) + K

(where K is an arbitrary constant)

By the fundamental theorem, the integral of F over the given path is

∫c F • dr = f (0, 1) - f (1, 0) = 5e ^(1/5) - 34/5

in the math equation 8 x 7 = 56, the 8 and the 7 are both factors of 56, since in this lesson we will use square tiles to figure out the factors of a whole find as many different arrays as you can, but follow one important rule: all the rows must have the i can make two rows of nine, so 2 and 9 are both factors of 18.

step-by-step explanation:

the answer is:

the lateral area is equal to

to find the lateral area of the square pyramid, first we need to find the perimeter of the base, and then, find the lateral area using the following formulas:

where,

s, is the base length

slant height, is the height of a the side of the pyramid

we are given:

now, calculating the perimeter of the base, we have:

then, calculating the lateral area:

hence, we have that the lateral area is equal to

have a nice day!