The functions f and g are integrable and f(x)dx :-5, = 7, and g(x)dx = 3. Use these to complete parts (a) through (f). 2 4 (Simplify your answer.) b. - 3 (Simplify your answer.)
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
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What is f?
![The functions \( f \) and \( g \) are integrable and
\[
\int_{2}^{4} f(x) \, dx = -5, \quad \int_{2}^{7} f(x) \, dx = 7, \quad \text{and} \quad \int_{2}^{7} g(x) \, dx = 3.
\]
Use these to complete parts (a) through (f).
b. \( \int_{2}^{4} g(x) \, dx = -3 \)
(Simplify your answer.)
c. \( \int_{2}^{7} 4g(x) \, dx = 12 \)
(Simplify your answer.)
d. \( \int_{4}^{7} f(x) \, dx = 12 \)
(Simplify your answer.)
e. \( \int_{2}^{7} [g(x) - f(x)] \, dx = -4 \)
(Simplify your answer.)
f. \( \int_{2}^{7} [2g(x) - f(x)] \, dx = \boxed{\,}\)
(Simplify your answer.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F70d1a455-c159-48a6-a4a3-cd41b63d10e2%2Ff7d93668-533e-45d8-a6c0-1e21dd08d5f6%2Fb179cq_processed.jpeg&w=3840&q=75)
![### Integral Calculations for Functions \( f(x) \) and \( g(x) \)
The functions \( f \) and \( g \) are integrable. The following integrals are provided:
\[
\int_{2}^{4} f(x) \, dx = -5, \quad \int_{2}^{2} f(x) \, dx = 7, \quad \int_{2}^{2} g(x) \, dx = 3
\]
Use these values to complete the following calculations:
#### a. \(\int_{4}^{4} f(x) \, dx = 0\)
(Simplify your answer.)
#### b. \(\int_{7}^{2} g(x) \, dx = -3\)
(Simplify your answer.)
#### c. \(\int_{2}^{7} 4g(x) \, dx = 12\)
(Simplify your answer.)
#### d. \(\int_{4}^{7} f(x) \, dx = 12\)
(Simplify your answer.)
#### e. \(\int_{2}^{7} [g(x) - f(x)] \, dx = -4\)
(Simplify your answer.)
These exercises involve evaluating and simplifying integrals based on given values. Understanding how to apply these can aid in solving complex integral equations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F70d1a455-c159-48a6-a4a3-cd41b63d10e2%2Ff7d93668-533e-45d8-a6c0-1e21dd08d5f6%2F533eh0i_processed.jpeg&w=3840&q=75)
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