"Evaluate the integrals ∫4y2dy" was answered by our community

druczekq4

Answered question

2021-11-22

Evaluate the integrals

\int \frac{4}{y^{2}} d y

Answer & Explanation

Eprint

Beginner2021-11-23Added 13 answers

Step 1
we have to evaluate the integral $\int \frac{4}{y^{2}} d y$
let the given integral be I.
therefore,
$I = \int \frac{4}{y^{2}} d y$
$= \int 4 y^{- 2} d y$
$= 4 \int y^{- 2} d y$
Step 2
as we know that $\int y^{n} d y = \frac{y^{n + 1}}{n + 1}$
therefore,
$I = 4 \int y^{- 2} d y$
$= 4 (\frac{y^{- 2 + 1}}{- 2 + 1}) + C$
$= 4 (\frac{y^{- 1}}{- 1}) + C$
$= - 4 y^{- 1} + C$
$= - \frac{4}{y} + C$
where C is constant of integration.
Step 3
therefore the value of the given integral $\int \frac{4}{y^{2}} d y i s \frac{- 4}{y} + C$

Drood1980

Beginner2021-11-24Added 16 answers

Step 1: Use Constant Factor Rule:

\int c f (x) d x = c \int f (x) d x

4 \int \frac{1}{y^{2}} d y

Step 2: Use Power Rule:

\int x^{n} d x = \frac{x^{n + 1}}{n + 1} + C

- \frac{4}{y}

Step 3: Add constant.

- \frac{4}{y} + C

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