What is the constant of proportionality of 8:5?
1 answer:
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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:
Answer:
(a)
(b)
Step-by-step explanation:
(a) can also be written as
x
the = ± y
Therefore :
= ±
since it was given that y < 0 , then the factor will be
(b) can also be written as :
x
Therefore , one of the factor is