Question

Integration:

Answer 1

\[\LARGE \int_{1/6}^{1/2} csc \pi t~cot \pi t~dt \]

Answer 2

It is 3.141592 ;)

#Blondgic

Answer 3

I told you the answer >o<

Answer 4

\(\large u = \sin (\pi t)\)

Answer 5

Seeeee.. That has pi in it ;o

Answer 6

\[\int \limits_{1/6}^{1/2} \csc \pi t~\cot \pi t~dt = \int \limits_{1/6}^{1/2} \frac{1}{\sin \pi t}~\frac{\cos \pi t}{\sin \pi t}~dt = \int \limits_{1/6}^{1/2} \frac{\cos \pi t}{\sin^2 \pi t}~dt\]

Answer 7

Let's simplify this a bit.
\[\int\limits_{1/6}^{1/2}\csc(\pi t)\cot(\pi t)dt=\int\limits_{1/6}^{1/2}(\frac{ 1 }{ \sin \pi t })(\frac{ \cos \pi t }{ \sin \pi t })dt=\int\limits_{1/6}^{1/2}\frac{ \cos \pi t }{ \sin^2\pi t } dt=\]

Answer 8

Use the substitution of \[u=\frac{ 1 }{ \sin \pi t }\]

Answer 9

\[du=\frac{ -\pi \cos \pi t }{ \sin^2 \pi t }dt \rightarrow -\frac{ 1 }{ \pi }du=\frac{ \cos \pi t }{ \sin^2 \pi t }dt\]

Answer 10

sorry. bad connection here.

Answer 11

\[\int\limits_{2}^{1}-\frac{ 1 }{ \pi }du=\left[ -\frac{ u }{ \pi } \right]_{2}^{1}=-\frac{ 1 }{ \pi }-(-\frac{ 2 }{ \pi })=\frac{ 1 }{ \pi }\]

Answer 12

1/6 changes to 2 because we made a substitution of u=1/sin(pi t)
u=1/sin(pi/6)=2

Using the same way, 1/2 changes to 1

Answer 13

In conclusion, the answer is 1/pi

Answer 14

Alrighty, thank you, and thanks for the explanation :)

Answer 15

welcome :)