Answered

Discover answers to your questions with Westonci.ca, the leading Q&A platform that connects you with knowledgeable experts. Get immediate and reliable solutions to your questions from a community of experienced experts on our Q&A platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

suppose that f is an even function, g is odd, both are integrable on [-5,5]..

Suppose That F Is An Even Function G Is Odd Both Are Integrable On 55 class=

Sagot :

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]

Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.