New Zealand
Level 8 - NCEA Level 3

# Integration to give log functions

## Interactive practice questions

The derivative of $f\left(x\right)$f(x) is $\frac{1}{x}$1x.

Which of the following could be the function? Select all the correct options.

$f\left(x\right)=k\ln x$f(x)=klnx

A

$f\left(x\right)=\ln\left(\left|kx\right|\right)$f(x)=ln(|kx|)

B

$f\left(x\right)=\ln kx$f(x)=lnkx for $k<0$k<0, $x>0$x>0

C

$f\left(x\right)=\ln x$f(x)=lnx

D

$f\left(x\right)=\ln kx$f(x)=lnkx for $k>0$k>0, $x<0$x<0

E

$f\left(x\right)=k\ln x$f(x)=klnx

A

$f\left(x\right)=\ln\left(\left|kx\right|\right)$f(x)=ln(|kx|)

B

$f\left(x\right)=\ln kx$f(x)=lnkx for $k<0$k<0, $x>0$x>0

C

$f\left(x\right)=\ln x$f(x)=lnx

D

$f\left(x\right)=\ln kx$f(x)=lnkx for $k>0$k>0, $x<0$x<0

E
Easy
Approx 2 minutes

State the primitive function of $\frac{6}{x}$6x.

Use $C$C as the constant of integration.

Determine $\int\frac{4}{x}dx$4xdx.

Use $C$C as the constant of integration.

Determine $\int\frac{-7}{x}dx$7xdx.

Use $C$C as the constant of integration.

### 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