Evaluate the following integrals : ∫(sin√x)/√x dx ​

Question

Evaluate the following integrals :

\(\int\)\(\frac{sin\sqrt x}{\sqrt x}\)dx

Answer 1

Assume ,

√x = t 

d(√x) = dt

⇒ \(\frac{1}{2\sqrt x}\) dx = dt

⇒ \(\frac{1}{\sqrt x}\) dx = dt

Substituting t and dt

⇒ 2∫ sint dt 

= - 2cost + c 

But,

√x = t 

⇒2 cos(√x) + c.