New Zealand
Level 8 - NCEA Level 3

# Fundamental Theorem of Calculus

## Interactive practice questions

The function $f$f has an antiderivative $F$F, and $F\left(3\right)=4$F(3)=4.

a

Express $\int_3^xf\left(t\right)dt$x3f(t)dt in terms of $F$F and $x$x.

b

Now, calculate $\frac{d}{dx}\int_3^xf\left(t\right)dt$ddxx3f(t)dt.

Easy
Approx 6 minutes

Consider the function $f\left(t\right)=-4t$f(t)=4t.

Consider the function $f\left(t\right)=12t+9$f(t)=12t+9.

Calculate $\frac{d}{dx}\int_2^x\left(6t^2-8t+3\right)dt$ddxx2(6t28t+3)dt.

### 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