Thread: 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.

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.

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

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

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

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