Since f(x) is even, we have:
[tex]\int ^5_{-5}f(x)dx=2\int ^5_0f(x)dx[/tex]
And since g(x) is odd, we have:
[tex]\int ^5_{-5}g(x)dx=0[/tex]
Now, using those results, we obtain:
[tex]\int ^5_{-5}\lbrack f(x)+g(x)\rbrack dx=\int ^5_{-5}f(x)dx+\int ^5_{-5}g(x)dx=2\int ^5_0f(x)dx+0=2\int ^5_0f(x)dx[/tex]
And since
[tex]\int ^5_0f(x)dx=19[/tex]
we obtain:
[tex]\int ^5_{-5}\lbrack f(x)+g(x)\rbrack dx=2\cdot19=38[/tex]
