### Home > CALC > Chapter 4 > Lesson 4.1.2 > Problem 4-22

4-22.

The value of

is*π*. Homework Help ✎

Without a calculator, find:

and . Use a graph to justify your conclusion.

Is *f*(*x*) = *x*sin(*x*) even, odd or neither?

*f*(*a*) = *a*sin(*a*)

*f*(−*a*) = −*a*sin(−*a*)

but, since *y* = sin*x* is odd,

= −*a*(−sin(*a*)) = *a*sin(*a*)

So *f*(*a*) = *f*(−*a*)

therefore, *y* = *x*sin*x* is even.

Use the eTool below to examine the graph.

Click the link at right for the full version of the eTool: Calc 4-22 HW eTool