document.write( "Question 344493: Please help me solve this equation. Evaluate the following definite integral: $\"+int%28+2%28cos+y%2B1%2Fy%29%2C+dy%2C+1%2C+pi+%29+\"$ \n" ); document.write( "

Algebra.Com's Answer #246494 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"+int%28+2%28cos+y%2B1%2Fy%29%2C+dy%2C+1%2C+pi+%29+\"$
\n" ); document.write( "Using some basic properties of integrals we can factor out the 2:
\n" ); document.write( " $\"+2%2Aint%28+%28cos+y%2B1%2Fy%29%2C+dy%2C+1%2C+pi+%29+\"$
\n" ); document.write( "and separate it into two:
\n" ); document.write( " $\"+2%2A%28int%28+cos%28+y%29%2C+dy%2C+1%2C+pi%29+%2B+int%28+1%2Fy%2C+dy%2C+1%2C+pi%29+%29+\"$
\n" ); document.write( "Now we have two fairly simple integrals. Since cos(y)dy integrates to sin(y) and (1/y)dy integrates to ln(y) we should get:
\n" ); document.write( " $\"+2%2A%28%28sin%28pi%29+-+sin%281%29%29+%2B+%28ln%28pi%29+-+ln%281%29%29%29\"$
\n" ); document.write( "Since $\"sin%28pi%29+=+0\"$ and ln(1) = 0:
\n" ); document.write( " $\"+2%2A%28%280+-+sin%281%29%29+%2B+%28ln%28pi%29+-+0%29%29\"$
\n" ); document.write( "Simplifying:
\n" ); document.write( " $\"+2%2A%28%28-+sin%281%29%29+%2B+%28ln%28pi%29%29%29\"$
\n" ); document.write( " $\"+-2sin%281%29+%2B+2ln%28pi%29\"$

\n" ); document.write( "If you need a decimal answer, then make sure your calculator is set to radian mode when you find sin(1).\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );