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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]

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