# Math Help - integrals, sin function and a denominator

1. ## integrals, sin function and a denominator

HI

Okay the goal is to evaluate this integral

integral sign (I will use S) (sin t^(1/2))/(t^1/2)

so if I let u = t^1/2 and du = dt/2(t^1/2)

S sin u / u du dt/du = I don't know what.

If it was just sin u I would know that it = - cos u + C but I don't know what to do with the denominator.

Please help me.

Calculus beginner

2. Originally Posted by calcbeg
HI

Okay the goal is to evaluate this integral

integral sign (I will use S) (sin t^(1/2))/(t^1/2)

so if I let u = t^1/2 and du = dt/2(t^1/2)

S sin u / u du dt/du = I don't know what.

If it was just sin u I would know that it = - cos u + C but I don't know what to do with the denominator.

Please help me.

Calculus beginner
$\int\frac{\sin\sqrt{t}}{\sqrt{t}}\,dt$

You made a good choice for $u$ but didn't sub it in correctly.

$u=\sqrt{t}$ and $du=\frac{1}{2\sqrt{t}}\,dt$

Now the integral is $2\int\sin(u)\,du = -2\cos(u)+C=\boxed{-2\cos(\sqrt{t})+C}$