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F(x)=|4x-20|

f(x)=F^(')(x)

int_(-5)^(5)f(x)dx=

$F(x)=|4 x-20|$ $\newline$ $f(x)=F^{\prime}(x)$ $\newline$ $\int_{-5}^{5} f(x) d x=$

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Evaluate a nonlinear function

Full solution

Q.

F(x)=|4 x-20|

\newline

f(x)=F^{\prime}(x)

\newline

\int_{-5}^{5} f(x) d x=

Find Derivative of F(x): First, we need to find the derivative of F(x) to get f(x), which is $F'(x)$ . $F(x) = |4x - 20|$ , so we need to consider two cases for the derivative since it's an absolute value function.
Consider Two Cases: Case $1$ : For x > 5, 4x - 20 > 0, so $F(x) = 4x - 20$ and $F'(x) = 4$ . Case $2$ : For x < 5, 4x - 20 < 0, so $F(x) = -(4x - 20)$ and $F'(x) = -4$ .
Integrate $f(x)$ Correctly: Now we need to integrate $f(x)$ from $-5$ to $5$ . But we made a mistake in the previous step, we should correct the cases for $x$ relative to $5$ .

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