Question #104687
x^3-\frac{2}{x^2}+2
(1,3)
1
Expert's answer
2020-03-11T09:32:17-0400

13(x32x2+2)dx\int^3_1(x^3-{2\above{2pt} x^2}+2)dx

=(x442x+2x)13=({x^4 \above{2pt} 4}-{2 \above{2pt} -x}+2x)|^3_1 =2(x2)2(x^{-2}) =2(x2+12+1)2({x^{-2+1}\above{2pt} -2+1})

=(341442(13+11)+2(31))=({3^4-1^4\above{2pt} 4}-2(-{1\above{2pt} 3}+{1 \above{2pt} 1})+2(3-1))

=(80142(1+33)+2(31))=({80-1 \above{2pt} 4}-2({-1+3 \above{2pt} 3})+2(3-1))

=(80443+4)=({80 \above{2pt} 4}-{4\above{2pt} 3}+4)

=(2043+4)=(20-{4 \above{2pt} 3}+4)

=(604+123)=({60-4+12\above{2pt} 3})

=683={68 \above{2pt} 3}

Answer: 683.\frac{68}{3}.


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