Find all the antiderivatives of the following function. Check your work by taking derivatives. h(y)=y^{-1}

Josalynn

Josalynn

Answered question

2021-04-18

Find all the antiderivatives of the following function. Check your work by taking derivatives.
h(y)=y1

Answer & Explanation

pivonie8

pivonie8

Skilled2021-04-20Added 91 answers

Step 1
To find the antiderivative of function h(y)=y1
Solution:
h(y)=y1
for finding antiderivative we need to integrate the given function:
y1dy=dyy
=ln|y|+C (using, dxx=ln|x|+C)
verification:
differentiating ln|y|+C w.r.t y we get
dydy(ln|y|+C)=1y=h(y) (using, ddx(lnx)=1x)
hence, verified
Step 2
Result:
Antiderivative: ln|y|+C
Jeffrey Jordon

Jeffrey Jordon

Expert2021-12-21Added 2605 answers

Answer is given below (on video)

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