# Trig Derivative - # 5

• Oct 22nd 2013, 11:35 PM
Jason76
Trig Derivative - # 5
$\int \cos\sqrt{7t} dt$

$\int \cos(7t)^{1/2} dt$

$\int \cos (u)^{1/2} dt$

$u = 7t$

$du = 7$

$\dfrac{1}{7}du = dt$

$\dfrac{1}{7}\int \cos u^{1/2}$

$\dfrac{1}{7}\int \dfrac{\sin u^{3/2}}{\dfrac{3}{2}} + C$

$(\dfrac{1}{7})(\dfrac{2}{3})\int \sin u^{3/2} + C$

$(\dfrac{1}{7})(\dfrac{2}{3})\int \sin u^{3/2} + C$

$\dfrac{2}{21}\int \sin u^{3/2} + C$

$\dfrac{2}{21}\int \sin 7t^{3/2} + C$
• Oct 23rd 2013, 12:10 AM
ibdutt
Re: Trig Derivative - # 5
• Oct 23rd 2013, 12:24 AM
Jason76
Re: Trig Derivative - # 5
I don't think integration by parts is the way, since it's only a Calculus I class. On that homework, we haven't even gotten to substitution yet.
• Oct 23rd 2013, 02:22 AM
ibdutt
Re: Trig Derivative - # 5