We have been given a table that shows a linear relationship between x and y. We are asked to find the rate of change change of y with respect to x.
To solve our given problem, we will find the slope of the line passing through the given points.
Let us find slope of line using points and
.
Therefore, the rate of change of y with respect to x is .
Answer:
Using either method, we obtain:
Step-by-step explanation:
a) By evaluating the integral:
The integral itself can be evaluated by writing the root and exponent of the variable u as:
Then, an antiderivative of this is:
which evaluated between the limits of integration gives:
and now the derivative of this expression with respect to "t" is:
b) by differentiating the integral directly: We use Part 1 of the Fundamental Theorem of Calculus which states:
"If f is continuous on [a,b] then
is continuous on [a,b], differentiable on (a,b) and
Since this this function is continuous starting at zero, and differentiable on values larger than zero, then we can apply the theorem. That means:
