Вычислите определённый интеграл:
[tex] \int\limits^3_1 {x^3} \, dx [/tex]
[tex] \int\limits^2_1 ({4^{5}-3x^{4}+3^{3}-1}) \, dx [/tex]
[tex] \int\limits^3_1 {x^3} \, dx [/tex]
[tex] \int\limits^2_1 ({4^{5}-3x^{4}+3^{3}-1}) \, dx [/tex]
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[1;2] ∫ (x^5 -3x^4 +x^3 -1) dx = (x^6/6 -3*x^5/5 + x^4/4 - x) [1;2] =
= 1/6 (2^6 -1^6) -3/5 (2^5 -1^5) +1/4 (2^4 -1^4) - (2-1) =
= 1/6 (2^6 -1^6) -3/5 (2^5 -1^5) +1/4 (2^4 -1^4) - (2-1) =
= 21/2 - 93/5 + 15/4 -1 = -107/20 = -5,35