Pertanyaan

Hasil dari ∫ t 3 2 t + 7 d t adalah.....

Hasil dari $\int t 3 2 t + 7 d t$ adalah.....

E. Nur

Master Teacher

Mahasiswa/Alumni Institut Teknologi Sepuluh Nopember

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah A.

Pembahasan

Rumus integral parsial adalah Misalkan Sehingga Dengan demikian hasil dari . Oleh karena itu, jawaban yang benar adalah A.

Rumus integral parsial adalah

integral U d V equals U V minus integral V d U

Misalkan

$table attributes columnalign right center left columnspacing 0px end attributes row U equals cell t rightwards arrow d U equals d t end cell row cell d V end cell equals cell cube root of 2 t plus 7 end root d t end cell row V equals cell integral cube root of 2 t plus 7 end root d t end cell row blank equals cell integral open parentheses 2 t plus 7 close parentheses to the power of 1 third end exponent d t end cell row blank equals cell 1 half times fraction numerator 1 over denominator begin display style 1 third end style plus 1 end fraction open parentheses 2 t plus 7 close parentheses to the power of 1 third plus 1 end exponent end cell row blank equals cell 1 half times 3 over 4 times open parentheses 2 t plus 7 close parentheses to the power of 4 over 3 end exponent end cell row blank equals cell 3 over 8 open parentheses 2 t plus 7 close parentheses to the power of 4 over 3 end exponent end cell end table$

Sehingga

$table attributes columnalign right center left columnspacing 0px end attributes row cell integral U d V end cell equals cell U V minus integral V d U end cell row cell integral t cube root of 2 t plus 7 end root d t end cell equals cell t times 3 over 8 open parentheses 2 t plus 7 close parentheses to the power of 4 over 3 end exponent minus integral 3 over 8 open parentheses 2 t plus 7 close parentheses to the power of 4 over 3 end exponent d t end cell row blank equals cell 3 over 8 t open parentheses 2 t plus 7 close parentheses to the power of 4 over 3 end exponent minus fraction numerator 3 over denominator 8 times 2 end fraction times fraction numerator 1 over denominator begin display style 7 over 3 end style end fraction open parentheses 2 t plus 7 close parentheses to the power of 4 over 3 end exponent end cell row blank equals cell 3 over 8 t open parentheses 2 t plus 7 close parentheses to the power of 4 over 3 end exponent minus 3 over 16 times 3 over 7 open parentheses 2 t plus 7 close parentheses to the power of 7 over 3 end exponent plus C end cell row blank equals cell 3 over 8 open parentheses 2 t plus 7 close parentheses to the power of 4 over 3 end exponent open parentheses t minus 3 over 14 open parentheses 2 t plus 7 close parentheses close parentheses plus C end cell row blank equals cell 3 over 8 open parentheses 2 t plus 7 close parentheses to the power of 4 over 3 end exponent open parentheses fraction numerator 14 t over denominator 14 end fraction minus fraction numerator 6 t over denominator 14 end fraction minus 21 over 14 close parentheses plus C end cell row blank equals cell 3 over 8 times 1 over 14 open parentheses 2 t plus 7 close parentheses to the power of 4 over 3 end exponent open parentheses 8 t minus 21 close parentheses plus C end cell row blank equals cell 3 over 112 open parentheses 2 t plus 7 close parentheses to the power of 4 over 3 end exponent open parentheses 8 t minus 21 close parentheses plus C end cell end table$

Dengan demikian hasil dari Error converting from MathML to accessible text. .

Oleh karena itu, jawaban yang benar adalah A.