Pertanyaan

Hiutnglah nilai integral berikut: a. ∫ 0 2 ( 2 x + 5 ) ( x − 3 ) d x + ∫ 2 4 ( 2 x + 5 ) ( x − 3 ) d x

Hiutnglah nilai integral berikut:

a. $\int_{0}^{2} (2 x + 5) (x - 3) d x + \int_{2}^{4} (2 x + 5) (x - 3) d x$ $\;$

A. Armanda

Master Teacher

Mahasiswa/Alumni Universitas Indraprasta PGRI

Jawaban terverifikasi

Jawaban

.

integral subscript 0 superscript 2 open parentheses 2 x plus 5 close parentheses open parentheses x minus 3 close parentheses space d x plus integral subscript 2 superscript 4 open parentheses 2 x plus 5 close parentheses open parentheses x minus 3 close parentheses space d x equals negative 25 1 third

Pembahasan

Ingat! Sehingga, Jadi, .

Ingat!

$table attributes columnalign right center left columnspacing 0px end attributes row cell integral subscript a superscript b f open parentheses x close parentheses plus-or-minus g open parentheses x close parentheses space d x end cell equals cell integral subscript a superscript b f open parentheses x close parentheses space d x plus-or-minus integral subscript a superscript b g open parentheses x close parentheses space d x end cell row cell integral subscript a superscript b k f open parentheses x close parentheses space d x end cell equals cell k integral subscript a superscript b f open parentheses x close parentheses space d x end cell row cell integral subscript a superscript b f open parentheses x close parentheses space d x end cell equals cell integral subscript a superscript k f open parentheses x close parentheses space d x plus integral subscript k superscript b f open parentheses x close parentheses space d x end cell row cell integral subscript a superscript b f open parentheses x close parentheses space d x end cell equals cell integral subscript a superscript k f open parentheses x close parentheses space d x minus integral subscript b superscript k f open parentheses x close parentheses space d x end cell row cell integral subscript a superscript b a x to the power of n space d x end cell equals cell open parentheses fraction numerator a over denominator n plus 1 end fraction x to the power of n plus 1 end exponent close parentheses subscript a superscript b end cell end table$

Sehingga,

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell integral subscript 0 superscript 2 open parentheses 2 x plus 5 close parentheses open parentheses x minus 3 close parentheses space d x plus integral subscript 2 superscript 4 open parentheses 2 x plus 5 close parentheses open parentheses x minus 3 close parentheses space d x end cell row blank equals cell integral subscript 0 superscript 4 open parentheses 2 x plus 5 close parentheses open parentheses x minus 3 close parentheses space d x end cell row blank equals cell integral subscript 0 superscript 4 open parentheses 2 x squared minus x minus 15 close parentheses space d x end cell row blank equals cell 2 integral subscript 0 superscript 4 x squared space d x minus integral subscript 0 superscript 4 x space d x minus integral subscript 0 superscript 4 15 space d x end cell row blank equals cell 2 open parentheses fraction numerator 1 over denominator 2 plus 1 end fraction x to the power of 2 plus 1 end exponent close parentheses subscript 0 superscript 4 minus open parentheses fraction numerator 1 over denominator 1 plus 1 end fraction x to the power of 1 plus 1 end exponent close parentheses subscript 0 superscript 4 minus open parentheses fraction numerator 15 over denominator 0 plus 1 end fraction x to the power of 0 plus 1 end exponent close parentheses subscript 0 superscript 4 end cell row blank equals cell 2 over 3 open parentheses x cubed close parentheses subscript 0 superscript 4 minus 1 half open parentheses x squared close parentheses subscript 0 superscript 4 minus 15 open parentheses x close parentheses subscript 0 superscript 4 end cell row blank equals cell 2 over 3 open parentheses 4 cubed minus 0 cubed close parentheses minus 1 half open parentheses 4 squared minus 0 squared close parentheses minus 15 open parentheses 4 minus 0 close parentheses end cell row blank equals cell fraction numerator 2 times 64 over denominator 3 end fraction minus 16 over 2 minus 15 times 4 end cell row blank equals cell 128 over 3 minus 8 minus 60 end cell row blank equals cell 128 over 3 minus 68 end cell row blank equals cell fraction numerator 128 minus open parentheses 68 times 3 close parentheses over denominator 3 end fraction end cell row blank equals cell fraction numerator negative 76 over denominator 3 end fraction end cell row blank equals cell negative 25 1 third end cell end table$

Jadi, integral subscript 0 superscript 2 open parentheses 2 x plus 5 close parentheses open parentheses x minus 3 close parentheses space d x plus integral subscript 2 superscript 4 open parentheses 2 x plus 5 close parentheses open parentheses x minus 3 close parentheses space d x equals negative 25 1 third .