Suppose $f (x)$ is a piecewise function defined as
$f (x) = 7 g (x)$ for $x < 4$
$f (x) = 8$ for $x \geq 4$
If $\int_{0}^{4} g (x) d x = 5$
then $\int_{0}^{21} f (x) d x =$

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Final Answer: $171$

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Step 1 ：Define the function $f (x)$ as a piecewise function: $f (x) = 7 g (x)$ for $x < 4$ and $f (x) = 8$ for $x \geq 4$

Step 2 ：Given that $\int_{0}^{4} g (x) d x = 5$

Step 3 ：Calculate the integral of $f (x)$ from 0 to 4: $\int_{0}^{4} f (x) d x = 7 \times \int_{0}^{4} g (x) d x = 7 \times 5 = 35$

Step 4 ：Calculate the integral of $f (x)$ from 4 to 21: $\int_{4}^{21} f (x) d x = 8 \times (21 - 4) = 136$

Step 5 ：Add the two parts to get the integral of $f (x)$ from 0 to 21: $\int_{0}^{21} f (x) d x = \int_{0}^{4} f (x) d x + \int_{4}^{21} f (x) d x = 35 + 136 = 171$

Step 6 ：Final Answer: $171$

Suppose f(x) is a piecewise function defined asf(x)=7g(x) for x<4f(x)=8 for x≥4If ∫04g(x)dx=5then ∫021f(x)dx=

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Suppose $f (x)$ is a piecewise function defined as
$f (x) = 7 g (x)$ for $x < 4$
$f (x) = 8$ for $x \geq 4$
If $\int_{0}^{4} g (x) d x = 5$
then $\int_{0}^{21} f (x) d x =$