Final answer:
Finding the bounds of a triple integral involves determining the limits within which the function is integrated, and for statistical elements like the confidence interval and error bound, statistical data and inverse probability functions are used.
Step-by-step explanation:
When finding the bounds of a triple integral, we are looking at the limits within which the function we are integrating is defined. Calculating the confidence interval and the error bound involves a bit of statistical knowledge and understanding how to use the data and distributions to define these intervals. Calculators and computers, such as the TI-83 and TI-84, can compute probabilities using functions like tcdf. For confidence intervals, inverse probability is used to find the t-value associated with a given probability.
In terms of a probability distribution, the area under the curve between bounds a and b gives you the probability that a random variable falls within that range. The area to the left of x (P(X < x)) is calculated for x values less than or equal to a, and the area to the right (P(X > x)) for x values greater than or equal to b. For calculation between two points c and d, it is the product of the base and height, (d – c)(b + a).
The area under a velocity-time graph represents displacement, whereas the gradient of a velocity-time graph indicates acceleration. In terms of motion, the gradient of a position-time graph provides the velocity.