\INT sin^4 2x . dx

Posted on 2006-04-20
Last Modified: 2008-03-17
How would I integrate sin to the power of 4 ?

I can integrate sin², so I figured I could rewrite it as:

  \INT (sin² 2x)² . dx

But now what?

I'm not looking for someone to solve this for me (although I do already have the correct answer with me), just to point me in the right direction..

Can anyone rewrite that in a form which would perhaps make it obvious of what I should do?

Surely there's no need to use the identity:

   \INT u(dv/dx) . dx = uv - \INT v(du/dx) . dx

for this?

Question by:InteractiveMind
    LVL 8

    Accepted Solution


    You can use the identity

    2 sin² t = 1 - cos 2t
    2 cos² t = 1 + cos 2t

    Hope these help.
    LVL 25

    Author Comment

    Oh yer, nice one. :)


    Featured Post

    What Security Threats Are You Missing?

    Enhance your security with threat intelligence from the web. Get trending threat insights on hackers, exploits, and suspicious IP addresses delivered to your inbox with our free Cyber Daily.

    Join & Write a Comment

    Suggested Solutions

    Title # Comments Views Activity
    Two list de-cypher 6 81
    Whisker Plot 1 32
    2k Power n formula 2 27
    Binomial distribution 2 42
    Complex Numbers are funny things.  Many people have a basic understanding of them, some a more advanced.  The confusion usually arises when that pesky i (or j for Electrical Engineers) appears and understanding the meaning of a square root of a nega…
    Lithium-ion batteries area cornerstone of today's portable electronic devices, and even though they are relied upon heavily, their chemistry and origin are not of common knowledge. This article is about a device on which every smartphone, laptop, an…
    In this sixth video of the Xpdf series, we discuss and demonstrate the PDFtoPNG utility, which converts a multi-page PDF file to separate color, grayscale, or monochrome PNG files, creating one PNG file for each page in the PDF. It does this via a c…
    This video discusses moving either the default database or any database to a new volume.

    730 members asked questions and received personalized solutions in the past 7 days.

    Join the community of 500,000 technology professionals and ask your questions.

    Join & Ask a Question

    Need Help in Real-Time?

    Connect with top rated Experts

    15 Experts available now in Live!

    Get 1:1 Help Now