Evaluate the following integrals :\(\int\)\(\frac{sin\sqrt x}{\sqrt x}

1.	Evaluate the following integrals :\(\int\)\(\frac{sin\sqrt x}{\sqrt x}\)dx
Answer» 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.

Evaluate the following integrals :\(\int\)\(\frac{sin\sqrt x}{\sqrt x}\)dx

Answer»

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.