How do you Integrate ?

2x01+sin(x2)dx

1 Answer
May 4, 2018

sin(x2)+cos(x2)1

Explanation:

2x01+sin(x2)dx

sin(x2)=2sin(x4)cos(x4)

1=sin2(x4)+cos2(x4)

Substitute

2x01+sin(x2)dx

=2x0sin2(x4)+2sin(x4)cos(x4)+cos2(x4)dx

By Completing The Square

=2x0(sin(x4)+cos(x4))2dx

=2x0(sin(x4)+cos(x4))dx

=[sin(x4)+cos(x4)]2x0

=sin(x2)+cos(x2)1

if this question was like this 1+cos(x2) it can be simplified to look like this

2cos(x4)using the Double angles Formulae