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Calculus/calculus integrals

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Expert: - 12/12/2008


Question
Can you please give me an example of an integral of polynomial?

Answer
To integrate any polynomial, for each term, raise the power of x by one and divide by the new exponet, but you asked for an example, so here it comes.
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Let f(x)=Ax+Bx²+Cx^3.  To integrate,

⌠
⌡f(x) dx = Ax²/2 + Bx^3/3 + Cx^4/4 + C.

Note how each term is divided by the new power.
The constant C is added on since we don't know what the constant was in f(x).

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For example, take f(x)=x²+4 and g(x)=x²+100.

The derivative of both functions is 2x, since the constants always disappear on differentiation.  If you integrate with limits, whatever the constant is, you get + and - the same constant, so it disappears.

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