`int_1^4 (sqrt(y) - y)/y^2 dy` Evaluate the integral

Expert Answers

An illustration of the letter 'A' in a speech bubbles

Hello!

Find the indefinite integral:

`int((sqrt(y)-y)/y^2)dy=int(y^(-3/2)-1/y)dy=(-2)*y^(-(1)/(2))-ln(y).`

Then substitute y from 1 to 4:

`(-2*4^(-1/2)-ln(4))-(-2)=-1-ln(4)+2=1-ln(4) approx -0.386.`

Approved by eNotes Editorial Team