{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

8.4.7-eg-1

# 8.4.7-eg-1 - Example Evaluate cos6 x dx 2 When the power of...

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Example Evaluate cos6 x dx. 2 When the power of sine or cosine is even, we write the integrand as the power of a square and use a double angle formula: cos6 x x = cos2 2 2 3 = 1 + cos 2 · x 2 2 3 = 1 (1 + cos(x))3 . 8 Expand the power and apply the double angle formula for the even power again: (1 + cos x)3 = 1 + 3 cos x + 3 cos2 x + cos3 x 1 + cos(2x) = 1 + 3 cos x + 3 + cos3 x. 2 Now integrate term by term, making the substitution u = sin x in the last integral, cos6 x 2 dx = 1 8 1 + 3 cos x + 3 1 + cos(2x) + cos3 x dx 2 = 1 3 3 x + 3 sin x + x + sin(2x) + 8 2 4 = 15 3 x + 3 sin x + sin(2x) + 82 4 = 15 3 1 x + 3 sin x + sin(2x) + sin x − sin3 x + C 82 4 3 = 5 1 3 1 x + sin x + sin(2x) − sin3 x + C. 16 2 32 24 (1 − sin2 x) cos x dx (1 − u2 ) du ...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online