Toronto Math Forum

MAT244--2018F => MAT244--Lectures & Home Assignments => Topic started by: chloe on November 11, 2018, 12:41:18 AM

Title: integral problems
Post by: chloe on November 11, 2018, 12:41:18 AM
\begin{equation}

\int \frac{-\sin{3t}\times9\sec^2{3t}}{3} \,dt\\

\end{equation}




Title: Re: integral problems
Post by: Chuanxin Zhang on November 11, 2018, 12:56:16 AM
\begin{equation}

\int \frac{-\sin{3t}\times9\sec^2{3t}}{3} \,dt\\

= \int \frac{-3sin{3t}}{cos^2{3t}} \,dt\\
=\int \frac{1}{cos^2{3t}} \,d(cos{3t})\\



\end{equation}



let  m=cos3t

\begin{equation}
\int \frac{1}{cos^2{3t}} \,d(cos{3t})\\
=\int \frac{1}{cos^2{3t}} \,dm\\
=\int \frac{1}{m^2}\,dm\\
=\frac{-1}{m}\\
=\frac{-1}{cos3t}\\


\end{equation}
Title: Re: integral problems
Post by: Victor Ivrii on November 11, 2018, 01:13:57 AM
$*$ IS N OT A SIGN OF MULTIPLICATION
Title: Re: integral problems
Post by: Chuanxin Zhang on November 11, 2018, 01:43:07 PM
Fixed! I thought * was the multiplication sign by default:(