Integration

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

Fundamental Theorem of Calculus

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

a

Express $\int_3^xf\left(t\right)dt$∫`x`3`f`(`t`)`d``t` in terms of $F$`F` and $x$`x`.

b

Now, calculate $\frac{d}{dx}\int_3^xf\left(t\right)dt$`d``d``x`∫`x`3`f`(`t`)`d``t`.

Easy

Approx 6 minutes

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

Apply integration methods in solving problems