Evaluate z c y 2 dx + z 2 dy + (1 − x 2 ) dz where c is the quarter of the circle of radius 1 in the xz–plane with center at the origin in the quadrant x ≥ 0, z ≤ 0, oriented counterclockwise when viewed from the positive y–axis, that is, looking in the −y direction.

Step-by-step explanation:

To find:

where, C is the quarter of the circle of radius 1 in the xz plane.

The center at origin.

where, because it is quarter circle.

The circle oriented counterclockwise when viewed from the positive y–axis.

Therefore,

If  x = cos t, then dx = -sin t dt

If  z = sin t, then dz = cos t dt

If y = 0 , then dy = 0

Substitute the value into integral.

Let

Change the integral limit and variable

Hence, the value of integral is

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: