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Integrating trigonometric functions for SQA Higher Maths

Integrating trigonometric functions

This page covers the following topics:

1. Integrating simple trigonometric functions

The integral of sinx is cosx and the integral of cosx is โˆ’sinx.

Integrating simple trigonometric functions

1

Calculate โˆซ15xยฒ + 8cos(4x)dx.

โˆซ15xยฒ + 8cos(4x)dx = 5xยณ + 2sin(4x) + c, where c is the constant of integration.

Calculate โˆซ15xยฒ + 8cos(4x)dx.

2

Calculate โˆซ20x + 12sin(2x)dx.

Using the Chain rule, โˆซ20x + 12sin(2x)dx = 10xยฒ โˆ’ 6cos(2x) + c, where c is the constant of integration.

Calculate โˆซ20x + 12sin(2x)dx.

3

What is the integral of 2sin(4x)?

โˆซ2sin(4x)dx = โˆ’cos(4x)/2 + c, where c is the constant of integration.

What is the integral of 2sin(4x)?

4

Find โˆซ2sinxdx.

โˆซ2sinxdx = โˆ’2cosx + c, where c is the constant of integration.

Find โˆซ2sinxdx.

5

Integrate the following: 24cos(4x).

โˆซ24cos(4x)dx = 6sin(4x) + c, where c is the constant of integration.

6sin(4x) + c

Integrate the following: 24cos(4x).

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