Expert: Paul Klarreich - 10/15/2008

Question
Evaluate the integral:  ∫ (2x4 + 3x2 – 2x) dx

Answer
Questioner:   Marie
Category:  Calculus
Private:  No
 
Subject:  Evaluating Integrals
Question:  Evaluate the integral:  ∫ (2x4 + 3x2 – 2x) dx
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Hi, Marie,

[Some day I will learn how to make those funny symbols.  Right now I don't trust the Allexperts site not to chew them up.]

Use the basic x^n rule:

{           x^(n+1)
| x^n dx =  ------- + c, for all n /= -1
}            n+1

And the rule for 'terms'

∫ (first + second) dx = ∫ first dx + ∫ second dx

In other words, if you have terms, just do them one at a time.


∫ (2x^4 + 3x^2 – 2x) dx

∫ 2x^4 dx =  2x^5/5

∫  3x^2 dx = 3x^3/3 = x^3

∫ (– 2x) dx = -2x^2/2 = -x^2

Just put them together now.