Integration

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

Properties of Definite Integrals

Consider the function $f\left(x\right)$`f`(`x`) as shown. The numbers in the shaded regions indicate the area of the region.

a

Determine $\int_{-3}^0f\left(x\right)dx$∫0−3`f`(`x`)`d``x`.

b

Determine the area enclosed by the curve and the $x$`x`-axis for $x<0$`x`<0.

c

Determine $\int_{-3}^2f\left(x\right)dx$∫2−3`f`(`x`)`d``x`.

d

Determine the area enclosed by the curve and the $x$`x`-axis.

Easy

Approx 2 minutes

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