Question

PLEASE HELP!!! I JUST NEED A STEP-BY-STEP!!!!!!

HINT: integrate with respect to y first (it is an easier approach)
∫∫5x sec^2(xy) dA; R={(x,y): 0 ≤ x ≤ π/6 , 0 ≤ y ≤ 2

[Answer] -5/2 ln(1/2)

Answer 1

Explanation:

`=5\displaystyle\int_(0)^(\pi/6)dx\displaystyle\int_(0)^(2)x\sec^2(xy)dy\\=5\displaystyle\int_(0)^(\pi/6)dx\displaystyle\int_(0)^(2)\sec^2(xy)d(xy)\\=5\displaystyle\int_(0)^(\pi/6)dx\tan(xy)|_(y=0)^(y=2)`

`=5\displaystyle\int_(0)^(\pi/6)\tan(2x)dx\\=-(5)/(2)\ln\cos(2x)|_(0)^(\pi/6)\\=-(5)/(2)[\ln\cos(\pi/3) - \ln\cos(0)]\\`

`=-(5)/(2)\ln{(1)/(2)`