Question

Evaluate the following integral: \int\frac{vdv}{6v^{2}-1}

Applications of integrals
ANSWERED
asked 2021-05-30
Evaluate the following integral: \(\int\frac{vdv}{6v^{2}-1}\)

Answers (1)

2021-05-31
Evaluate as follows:
Substitute \(6v^{2}-1=t\)
Differentiate with respect to v,
\(12v=\frac{dt}{dv}\)
\(vdv=\frac{dt}{12}\)
Thus, the integral is calculated as:
\(I=\int \frac{vdv}{6v^{2}-1}\)
\(=\int \frac{dt}{12t}\)
\(=\frac{1}{12}\log|t|+c\)
\(=\frac{1}{12}\log|6v^{2}-1|+c\)
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