Question 344493
{{{ int( 2(cos y+1/y), dy, 1, pi ) }}}
Using some basic properties of integrals we can factor out the 2:
{{{ 2*int( (cos y+1/y), dy, 1, pi ) }}}
and separate it into two:
{{{ 2*(int( cos( y), dy, 1, pi) + int( 1/y, dy, 1, pi) ) }}}
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:
{{{ 2*((sin(pi) - sin(1)) + (ln(pi) - ln(1)))}}}
Since {{{sin(pi) = 0}}} and ln(1) = 0:
{{{ 2*((0 - sin(1)) + (ln(pi) - 0))}}}
Simplifying:
{{{ 2*((- sin(1)) + (ln(pi)))}}}
{{{ -2sin(1) + 2ln(pi)}}}<br>
If you need a decimal answer, then make sure your calculator is set to radian mode when you find sin(1).