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Chapter 11: Problem 20

Find the indefinite integral and check your result by differentiation. $$ \int v^{-1 / 2} d v $$

Short Answer

Expert verified
The indefinite integral of \(v^{-1/2}\) is \(2\sqrt{v} + C\).

Step by step solution

01

Apply the Power Rule for Integration

When the power of the variable v is a real number, the power rule for integration can be applied. This integral should be computed as follows: \[\int v^{-1/2} dv = 2\sqrt{v} + C\] where C is the arbitrary constant of integration.
02

Differentiate the integral

To verify the computed integral, differentiate it which should result in the initial function. The derivative of \(2\sqrt{v}\) using the power rule for differentiation is \(v^{-1/2}\) . This checks out since it is the same as the integrand function.

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