New Zealand
Level 8 - NCEA Level 3

# Indefinite and definite integrals (e^(f(x) non-linear)

## Interactive practice questions

Consider the function $y=e^{x^3}$y=ex3.

a

Find the derivative $\frac{dy}{dx}$dydx.

b

Hence find the value of $\int3x^2e^{x^3}dx$3x2ex3dx.

You may use $C$C to represent the constant of integration.

Easy
Approx 2 minutes

Consider the function $y=e^{3x^4+4}$y=e3x4+4.

Consider the function $y=e^{3x^4-5}$y=e3x45.

Determine the value of $\int\left(4x^3+3\right)e^{x^4+3x}dx$(4x3+3)ex4+3xdx.

### 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