I'm reading this as

with

.
The value of the integral will be independent of the path if we can find a function

that satisfies the gradient equation above.
You have

Integrate

with respect to

. You get


Differentiate with respect to

. You get
![\dfrac{\partial f}{\partial y}=\dfrac{\partial}{\partial y}[x^2e^{-y}+g(y)]](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cpartial%20f%7D%7B%5Cpartial%20y%7D%3D%5Cdfrac%7B%5Cpartial%7D%7B%5Cpartial%20y%7D%5Bx%5E2e%5E%7B-y%7D%2Bg%28y%29%5D)


Integrate both sides with respect to

to arrive at



So you have

The gradient is continuous for all

, so the fundamental theorem of calculus applies, and so the value of the integral, regardless of the path taken, is
1. Answer x=-5
You would subtract 25 from each side of the equal sign, taking 25 away from 40 and 25 away from 25, isolating the x. So you would then have -3x=15. You would then divide each side by -3, and getting x=-5
2x + 21 = 35
hope this helps
362.50 for tennis and golf balls.
To find the answer divide the dollar amount by how many cans or boxes each cost then multiply that answer by the total amount purchased.
Golf balls
45/2=22.50 each box
22.5*5=112.50 total
Tennis balls
30/12=2.50 each can
2.50*100 = 250.00
add the dollar amounts together
112.50+250.00 =362.50