What is Q3 for this data set?
2 answers:
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The reason the "+ C" is not needed in the antiderivative when evaluating a definite integral is; The C's cancel each other out as desired.
<h3>How to represent Integrals?</h3>
Let us say we want to estimate the definite integral;
I =
Now, for any C, f(x) + C is an antiderivative of f′(x).
From fundamental theorem of Calculus, we can say that;
where Ф(x) is any antiderivative of f'(x). Thus, Ф(x) = f(x) + C would not work because the C's will cancel each other.
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The idea is to use the tangent line to at
in order to approximate
.
We have
so the linear approximation to is
Hence and
.
Then
Answer:
g(x) = sinh^-1 ( ln(7x^6 +3) / sqrt( 8+cot( x^( 3+x))))
Step-by-step explanation:
Using the fundamental theorem of calculus
Taking the derivative of the integral gives back the function
Since the lower limit is a constant when we take the derivative it is zero
d/dx
g(t) = sinh^-1 ( ln(7t^6 +3) / sqrt( 8+cot( t^( 3+t))))
Replacing t with x
g(x) = sinh^-1 ( ln(7x^6 +3) / sqrt( 8+cot( x^( 3+x))))