Answered

At Westonci.ca, we provide clear, reliable answers to all your questions. Join our vibrant community and get the solutions you need. Get quick and reliable answers to your questions from a dedicated community of professionals on our platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

find out volume of the solid obtained by rotating the region bounded by the given curves about the specified line. y=lnx, y=1, y=3,x=0; about the y-axis.

Sagot :

[tex]Look\ at\ the\ picture.\\\\y=lnx\\\\x=lny\to e^x=e^{lny}\to y=e^x\\\\V=\int\limits_1^3\left(e^x\right)^2dx=(*)\\\\\int\left(e^x\right)^2dx=\int(e^x\times e^x)dx\Rightarrow \left|\begin{array}{ccc}e^x=t\\\\e^x\ dx=dt\end{array}\right|\Rightarrow\int\limits_1^3t\ dt=\frac{1}{2}t^2=\frac{1}{2}\left(e^x\right)^2=\frac{e^{2x}}{2}[/tex]

[tex](*)=\left\frac{e^{2x}}{2}\right]^3_1=\frac{e^{2(3)}}{2}-\frac{e^{2(1)}}{2}=\frac{e^6-e^2}{2}\ (units)[/tex]
View image Аноним
Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.