Question

For \[\int_4^9\frac{\sqrt{x}}{(30-x^{\frac32})^2}\,dx,\] which substitution is used?

पर्याय

• \[(30-x^{\frac32})^2=t\]

• \[30-x^{\frac32}=t\]

• \[x^{\frac32}=t\]

• \[\sqrt{x}=t\]

Answer 1

The substitution is \(30-x^{\frac32}=t\).
It changes the denominator \((30-x^{\frac32})^2\) into \(t^2\), allowing the integral to be written in terms of \(t\).