Question

integration of dv / 100 - 4v2​

Answer 1

Step-by-step explanation:

We have,

$\int \frac{dv}{100 - 4 {v}^{2} }$

$= \frac{1}{4} \int \frac{dv}{25 - {v}^{2} }$

$= \frac{1}{4} \int \frac{dv}{ {(5)}^{2} - {(v)}^{2} }$

$= \frac{1}{4} . \frac{1}{10} ln | \frac{5 - v}{5 + v} | + c$

Answer 2

Answer:

We have,

\begin{gathered} \int \frac{dv}{100 - 4 {v}^{2} } \\ \end{gathered}

∫

100−4v

2

dv

\begin{gathered} = \frac{1}{4} \int \frac{dv}{25 - {v}^{2} } \\ \end{gathered}

=

4

1

∫

25−v

2

dv

\begin{gathered} = \frac{1}{4} \int \frac{dv}{ {(5)}^{2} - {(v)}^{2} } \\ \end{gathered}

=

4

1

∫

(5)

2

−(v)

2

dv

\begin{gathered} = \frac{1}{4} . \frac{1}{10} ln | \frac{5 - v}{5 + v} | + c \\ \end{gathered}

=

4

1

.

10

1

ln∣

5+v

5−v

∣+c