if f(x) = g(x) + 7 for 3 <= x <= 5 , then integrate [f(x) + g(x)] dx from 3 to 5 = ?
To find the integral of [f(x) + g(x)] over the interval from 3 to 5, we need to first find the integral of f(x) + g(x).
Since f(x) = g(x) + 7, we can substitute this into the integral:
∫[f(x) + g(x)] dx from 3 to 5 = ∫[(g(x) + 7) + g(x)] dx from 3 to 5.
Expanding the expression inside the integral:
= ∫[2g(x) + 7] dx from 3 to 5.
Now, we can integrate term by term:
= ∫2g(x) dx + ∫7 dx from 3 to 5.
The integral of 2g(x) will depend on the specific function g(x) and cannot be determined without knowing its form.
However, the integral of the constant term 7 is simply 7x:
= 2∫g(x) dx + 7x from 3 to 5.
Now, if you know the specific form of g(x), you can determine the integral of g(x) and substitute the limits of integration from 3 to 5 to evaluate the integral.
To find the integral of [f(x) + g(x)] from 3 to 5, we need to integrate f(x) and g(x) separately and then add them together.
Given that f(x) = g(x) + 7, we can rewrite [f(x) + g(x)] as (g(x) + 7) + g(x), which simplifies to 2g(x) + 7.
Now, let's find the integral of 2g(x) + 7 from 3 to 5.
1. First, find the integral of 2g(x):
∫(2g(x)) dx = 2∫g(x) dx
2. Then, find the integral of g(x):
∫g(x) dx
3. Finally, add the result to the integral of 2g(x):
2∫g(x) dx + 7
Note: Without the specific function g(x), we cannot determine the exact value of the integral. Please provide the function g(x) for more accurate results.