Write the integral as a sum of integrals without absolute values and evaluate:&nbsp;∫−63|x|3&nbsp;dx&nbsp;

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Write the integral as a sum of integrals without absolute values and evaluate:&amp;nbsp;∫−63|x|3&amp;nbsp;dx&amp;nbsp;

Amubbemibren3k · Accepted Answer

Compute the definite integral:  ∫−63|x|3dx  When 0&amp;lt;x&amp;lt;3, x is positive.   This means |x|3=x3=x3.   When −6&amp;lt;x&amp;lt;0, x is negative.   This means |x|3=(−x)3=−x3:  =∫−60−x3dx+∫03x3dx  Factor out constants:  =−∫−60x3dx+∫03x3dx  Apply the fundamental theorem of calculus.  The antiderivative of x3 is x44:  =(−x44)∣−60+∫03x3dx  Evaluate the antiderivative at the limits and subtract.  (−x44)∣−60=(−044)−(−14(−6)4)=324:  =324+∫03x3dx  Apply the fundamental theorem of calculus.  The antiderivative of x3 is x44:  =324+x44∣03  Evaluate the antiderivative at the limits and subtract.  x44∣03=344−044=814:  Answer:   =13774

Write the integral as a sum of integrals without absolute

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