New Zealand
Level 8 - NCEA Level 3

# Integration of Sine and Cosine

## Interactive practice questions

State a primitive function of $6\sin x-\cos x$6sinxcosx.

You may use $C$C as a constant.

Easy
Approx a minute

Determine $\int\left(x^{\frac{1}{4}}+\sin3x\right)dx$(x14+sin3x)dx.

You may use $C$C as the constant of integration.

Determine $\int\left(\cos x-\sin3x\right)dx$(cosxsin3x)dx.

You may use $C$C as the constant of integration.

Determine $\int\left(\sin\left(\frac{x}{3}\right)+\cos\left(\frac{x}{3}\right)\right)dx$(sin(x3)+cos(x3))dx.

You may 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