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
Hello,
Answer is Dsince y=k(x-2)²-5 and if k=1 ==>D.
Answer:
Step-by-step explanation to be honest probably 12 if not i’m so sorry
Answer:
what's the question
Step-by-step explanation:
is there a photo you can post we need more info
Okay, move the decimal behind the 8. There are 4 places before the decimal so it is nagitive. If there are places Infront of the decimal is nagitive. So the answer is 8.235×10-4