∫13(x3−2x2+2)dx\int^3_1(x^3-{2\above{2pt} x^2}+2)dx∫13(x3−x22+2)dx
=(x44−2−x+2x)∣13=({x^4 \above{2pt} 4}-{2 \above{2pt} -x}+2x)|^3_1=(4x4−−x2+2x)∣13 =2(x−2)2(x^{-2})2(x−2) =2(x−2+1−2+1)2({x^{-2+1}\above{2pt} -2+1})2(−2+1x−2+1)
=(34−144−2(−13+11)+2(3−1))=({3^4-1^4\above{2pt} 4}-2(-{1\above{2pt} 3}+{1 \above{2pt} 1})+2(3-1))=(434−14−2(−31+11)+2(3−1))
=(80−14−2(−1+33)+2(3−1))=({80-1 \above{2pt} 4}-2({-1+3 \above{2pt} 3})+2(3-1))=(480−1−2(3−1+3)+2(3−1))
=(804−43+4)=({80 \above{2pt} 4}-{4\above{2pt} 3}+4)=(480−34+4)
=(20−43+4)=(20-{4 \above{2pt} 3}+4)=(20−34+4)
=(60−4+123)=({60-4+12\above{2pt} 3})=(360−4+12)
=683={68 \above{2pt} 3}=368
Answer: 683.\frac{68}{3}.368.
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