Question

Suppose that f is an even function, g is odd, both are integrable on [-7, 7], and we know that….

Answer 1

SOLUTION:

Step 1:

In this question, we have given the following:

Step 2:

The details of the solution are as follows:

Suppose that f is an even function, g is odd, both are integrable on [-7, 7], and we know that:

$\begin{gathered} \int ^7_0f(x)dx\text{ = 5, Recall that f(x) is an even function} \\ \text{Then} \\ \int ^7_{-7}f(x)dx\text{ = 2 ( 5 ) = 10} \end{gathered}$$\begin{gathered} \int ^7_0g(x)dx\text{ = 4. 5 , Recall that g(x) is an odd function} \\ \text{Then } \\ \int ^7_{-7}g(x)dx\text{ =4. 5 - 4. 5 }=\text{ 0} \end{gathered}$

Finally, we can see that:

$\int ^7_{-7}\lbrack\text{ f(x) + g ( x) }\rbrack dx\text{ = 10 + 0 = 10}$