Find the area of the region under the graph of the function $f$ on the interval $[0,6]$.
\[
f(x)=6 x-x^{2}
\]
square units

Answer

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Final Answer: The area under the curve of the function $f(x)=6x-x^2$ from 0 to 6 is $\boxed{36}$ square units.

Steps

Step 1 ：The area under the curve of a function from a to b is given by the definite integral of the function from a to b. In this case, we need to find the definite integral of the function $f(x)=6x-x^2$ from 0 to 6.

Step 2 ：The area under the curve of the function $f(x)=6x-x^2$ from 0 to 6 is 36 square units.

Step 3 ：Final Answer: The area under the curve of the function $f(x)=6x-x^2$ from 0 to 6 is $\boxed{36}$ square units.

Find the area of the region under the graph of the function $f$ on the interval $[0,6]$.\[f(x)=6 x-x^{2}\]square units

Answer

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Find the area of the region under the graph of the function $f$ on the interval $[0,6]$.
\[
f(x)=6 x-x^{2}
\]
square units