Determine the interval on which f(x)=square root of x+ 2 is integrable
1) (negative infinite, 2)
2) (-2, infinite)
3) (-infinite, -2) U (-2, infinite)
4) All reals
I assume you mean f(x) = √(x+2)
f is only defined on [-2,∞), since we need x+2 >= 0
Since it also continuous, it is integrable on the same interval.
To determine the interval on which the function f(x) = √(x + 2) is integrable, we need to check if the function is defined for all values within a certain interval.
In this case, the function √(x + 2) is defined for all values of x as long as the expression inside the square root, x + 2, is non-negative.
To find the interval, we need to solve the inequality x + 2 ≥ 0.
x + 2 ≥ 0
x ≥ -2
From this inequality, we can see that x must be greater than or equal to -2 for the function to be defined.
Therefore, the interval on which f(x) = √(x + 2) is integrable is (-2, ∞).
Hence, the correct option is 2) (-2, infinite).