# Exam-style Questions: Integration

**1. a)** By using the substitution u = 4- sin x, or otherwise, find

**b)** Hence, or otherwise, find

**(Marks available: 6)**

**Answer outline and marking scheme for question: 1**

**Give yourself marks for mentioning any of the points below:**

**a)** u = 4 - sin x, therefore du = (-) cos x dx.

**Substitute u into the given equation gives:**

**Integrating this gives:**

**Therefore:**

**(4 marks)**

**b)** Use u = 2x, therefore 1/2 du = dx

Substitute u into the given equation and integrating gives:

**(2 marks)**

**(Marks available: 6)**