New Zealand
Level 8 - NCEA Level 3

Properties of Definite Integrals

Interactive practice questions

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$03f(x)dx.

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$23f(x)dx.

d

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

Easy
Approx 2 minutes

Suppose $\int_4^6f\left(x\right)dx=3$64f(x)dx=3.

Consider the function $f\left(x\right)$f(x) where $\int_{-1}^6f\left(x\right)dx=3$61f(x)dx=3.

Outcomes

M8-11

Choose and apply a variety of differentiation, integration, and antidifferentiation techniques to functions and relations, using both analytical and numerical methods

91579

Apply integration methods in solving problems