calculation: find the area of ​​the surface formed by turning the given curve around $ (i) x axis and $ (i) y axis

Q: Find the area of ​​the formed surface by rotating the given curve around $ (i) x-axis $ Y $ (i) y-axis $
$$ x = a cos theta, y = b without theta, 0 le theta le2 pi $$

About $ x- $axis is $ S = 2 pi int_0 ^ {2 pi} b without theta sqrt {a ^ 2 ( without theta) ^ 2 + b ^ 2 ( cos theta) ^ 2} d theta $
About $ y- $axis is $ S = 2 pi int_0 ^ {2 pi} to cos theta sqrt {a ^ 2 ( without theta) ^ 2 + b ^ 2 ( cos theta) ^ 2} d theta $
from now on I'm stuck. I can not decipher the integral part. Any suggestion or solution will be appreciated.
Thanks in advance.