Integration

NZ Level 8 (NZC) Level 3 (NCEA) [In development]

Signed area function

Consider the function $f\left(x\right)=8-4x$`f`(`x`)=8−4`x`.

a

Graph the function.

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b

What is the $x$`x`-coordinate of the $x$`x`-intercept?

c

Let $F\left(x\right)$`F`(`x`) be the area function representing the area bound by $f\left(x\right)$`f`(`x`) and the $x$`x`-axis for $x<2$`x`<2.

Integrate $f\left(x\right)$`f`(`x`) to find an expression for $F\left(x\right)$`F`(`x`).

Use $C$`C` as the constant of integration.

Easy

Approx 2 minutes

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