true or false?

Question

∫xcosxdx= ( (x²)/2 )sinx+C

 

true or false

Answer 1

Do you like doing things the hard way or the easy way?  Since we need to see if this equation is true or not, we can either take the hard way by using integration by parts to integrate which will take time, or we can take the easy way and derive the right side of the equation which we can do in 5 seconds.  We should end up with the left side.

 

 

Derive  ((1/2)x²)sinx + C

 

 

Using the product rule,

 

xsinx + (1/2)x² (cosx)

 

 

This does not equal the left side of the equation.  The integration is false.