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Advanced Math/Calculus: Techniques of Integration

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Expert: Sherry Wallin - 7/15/2009


Question
Use trignometric identities to simply the function and then integrate with respect to x

i. sin^4 x

Thanks for the help

Answer
Hi William~
    It isn't necessary to use a trigonometric identity to integrate this problem. You can use a formula from a table of integrals. Not only that there isn't an identity that would simplify this integration. You know that sin^2x + cos^2x = 1 so sin^2x = 1 - cos^2x so sin^4x = (1-cos^2x)^2 but this is not helpful and only makes it more complicated.
Use int(sin^n u du) =
-(1/n)sin^(n-1)u*cosu+[(n-1)/n]*int(sin^(n-2)u du)
and for the int(sin^2u du) use (1/2)u -(1/4)sin2u

resulting in (-1/4)sin^3x*cosx+(3/4)[(1/2)x -(1/4)sin2x
= (-1/4)sin^3x*cosx +(3/8)x-(3/16)sin2x

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Sherry Wallin

Expertise

I can answer most questions up through Calculus and some in Number Theory and Abstract Algebra.

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I have had my Bachelor's Degree since 1987 and have been a teacher since 1988. I earned my Masters Degree in Mathematics May 2010. I have been teaching at the same community college since 2002.

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I have taught 12 years at the community college level, medical college, and technical college as well as a high school instructor and alternative education instructor and charter school instructor.

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Master's GPA 3.56 Bachelor's GPA 3.34 Post grad work not degree related GPA 4.0

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