Note that √(4 - t²) is defined only as long as 4 - t² ≥ 0, or -2 ≤ t ≤ 2. Then the real integral exists only if -2 ≤ x ≤ 2. (Otherwise we deal with complex numbers.)
If x = 2, then the integral corresponds to the area of a quarter-circle with radius 2. This means that the integral has a maximum value of 1/4 • π • 2² = π.
On the opposite end, if x = -2, then the integral has the same value, but the integral from 0 to -2 is equal to the negative integral from -2 to 0. So the minimum value is -π.
For all x in between, we observe that the integrand is continuous over the rest of its domain, so F(x) is continuous.
Then the range of F(x) is the interval [-π, π].
Answer:
less than
Step-by-step explanation:
think of it as an aliigator who wants cookies. The alligator is. going to eat the side with more cookies. if he is not facing one side that means that it is lees than
Answer: both our A
Step-by-step explanation:
The equation of the line is given by
y = mx + c
where m is the gradient of the line
c is where the line cuts the y-axis
x & y represent coordinates on the line.
The gradient m can be obtained as follows:
m = (5 - 8) / (5 - - 10) = (-3) / (15) = - 1/5
To obtain c, we use any known coordinate on the line and substitute it as well as the gradient in the general equation for the line.
Taking coordinates (5,5)
5 = (- 1/5)(5) + c
5 = - 1 + c
c = 6
Hence, the equation for this line is
y = -x/5 + 6
