## Integrals: indefinite integral (1-cos(t/6))^6 sin(t/6) dt

Limits, differentiation, related rates, integration, trig integrals, etc.
doggy
Posts: 10
Joined: Thu Apr 16, 2009 12:17 am
Contact:

### Integrals: indefinite integral (1-cos(t/6))^6 sin(t/6) dt

How do I evaluate the indefinite integral (1-cos(t/6))^6 sin(t/6)?

Would I use a u substitution of u= sin(t/6)?

Martingale
Posts: 333
Joined: Mon Mar 30, 2009 1:30 pm
Location: USA
Contact:

### Re: Integrals

How do I evaluate the indefinite integral (1-cos(t/6))^6 sin(t/6)?

Would I use a u substitution of u= sin(t/6)?
$\int (1-cos(\frac{t}{6}))^6 sin(\frac{t}{6})dt$

how about $u=1-cos(\frac{t}{6})$

doggy
Posts: 10
Joined: Thu Apr 16, 2009 12:17 am
Contact:

### Re: Integrals: indefinite integral (1-cos(t/6))^6 sin(t/6) dt

So then the answer would be (u^7/7)(6u) = ((1-cos(t/6))^7/7)(6(1-cos(t/6))

Martingale
Posts: 333
Joined: Mon Mar 30, 2009 1:30 pm
Location: USA
Contact:

### Re: Integrals: indefinite integral (1-cos(t/6))^6 sin(t/6) dt

So then the answer would be (u^7/7)(6u) = ((1-cos(t/6))^7/7)(6(1-cos(t/6))

$\int (1-cos(\frac{t}{6}))^6 sin(\frac{t}{6})dt$

how about $u=1-cos(\frac{t}{6})$

$du=sin(\frac{t}{6})\cdot\frac{1}{6}dt$

so

$6du=sin(\frac{t}{6})dt$

$\int (1-cos(\frac{t}{6}))^6 sin(\frac{t}{6})dt=6\int (u)^6du=\cdots$

Return to “Calculus”