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प्रश्न
Under the substitution \[30-x^{\frac32}=t,\] what is the correct expression for \(\sqrt{x}\,dx\)?
पर्याय
\[\sqrt{x}\,dx=-\frac23\,dt\]
\[\sqrt{x}\,dx=\frac23\,dt\]
\[\sqrt{x}\,dx=2\,dt\]
\[\sqrt{x}\,dx=-\frac32\,dt\]
MCQ
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उत्तर
Differentiating \(30-x^{\frac32}=t\) gives \(-\frac32\sqrt{x}\,dx=dt\).
Solving for \(\sqrt{x}\,dx\) gives \(-\frac23\,dt\).
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