Integrating trigonometric functions for SQA Higher Maths

This page covers the following topics:

1. Integrating simple trigonometric functions

The integral of sinx is cosx and the integral of cosx is −sinx.

1

Calculate ∫15x² + 8cos(4x)dx.

∫15x² + 8cos(4x)dx = 5x³ + 2sin(4x) + c, where c is the constant of integration.

Calculate ∫20x + 12sin(2x)dx.

Using the Chain rule, ∫20x + 12sin(2x)dx = 10x² − 6cos(2x) + c, where c is the constant of integration.

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

∫2sin(4x)dx = −cos(4x)/2 + c, where c is the constant of integration.

Find ∫2sinxdx.

∫2sinxdx = −2cosx + c, where c is the constant of integration.

Integrate the following: 24cos(4x).

∫24cos(4x)dx = 6sin(4x) + c, where c is the constant of integration.

6sin(4x) + c

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