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Hitunglah hasil dari integral tentu berikut ini:

Pertanyaan

Hitunglah hasil dari integral tentu berikut ini:

integral subscript negative 2 end subscript superscript 1 open parentheses x cubed minus 3 x squared plus 5 x plus 2 close parentheses d x

Pembahasan Soal:

Ingatlah bahwa

integral subscript a superscript b f open parentheses x close parentheses d x equals straight F open parentheses b close parentheses minus straight F open parentheses a close parentheses

dengan straight F open parentheses x close parentheses adalah anti turunan dari f open parentheses x close parentheses.

Maka

table attributes columnalign right center left columnspacing 0px end attributes row cell integral subscript negative 2 end subscript superscript 1 open parentheses x cubed minus 3 x squared plus 5 x plus 2 close parentheses d x end cell equals cell right enclose 1 fourth x to the power of 4 minus x cubed plus 5 over 2 x squared plus 2 x end enclose subscript negative 2 end subscript superscript 1 end cell row blank equals cell open parentheses 1 fourth open parentheses 1 close parentheses to the power of 4 minus open parentheses 1 close parentheses cubed plus 5 over 2 open parentheses 1 close parentheses squared plus 2 open parentheses 1 close parentheses close parentheses end cell row blank blank cell negative open parentheses 1 fourth open parentheses negative 2 close parentheses to the power of 4 minus open parentheses negative 2 close parentheses cubed plus 5 over 2 open parentheses negative 2 close parentheses squared plus 2 open parentheses negative 2 close parentheses close parentheses end cell row blank equals cell open parentheses 1 fourth open parentheses 1 close parentheses minus 1 plus 5 over 2 open parentheses 1 close parentheses plus 2 close parentheses end cell row blank blank cell negative open parentheses 1 fourth open parentheses 16 close parentheses minus open parentheses negative 8 close parentheses plus 5 over 2 open parentheses 4 close parentheses minus 4 close parentheses end cell row blank equals cell open parentheses 1 fourth minus 1 plus 5 over 2 plus 2 close parentheses minus open parentheses 4 plus 8 plus 10 minus 4 close parentheses end cell row blank equals cell open parentheses 1 fourth minus 4 over 4 plus 10 over 4 plus 8 over 4 close parentheses minus 18 end cell row blank equals cell 15 over 4 minus 72 over 4 end cell row blank equals cell negative 57 over 4 end cell end table

Jadi, nilai dari integral subscript negative 2 end subscript superscript 1 open parentheses x cubed minus 3 x squared plus 5 x plus 2 close parentheses d x equals negative 57 over 4.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

A. Acfreelance

Terakhir diupdate 03 Mei 2021

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Pertanyaan yang serupa

Pembahasan Soal:

Soal tersebut tidak dapat dikerjakan karena batas atas lebih kecil dari batas bawah, kemungkinan yang dimaksud dalam soal

  begin mathsize 14px style integral subscript 2 superscript 4 6 x squared minus 6 x minus 1 d x equals... end style

Sehingga apabila soal tersebut diselesaikan

 begin mathsize 14px style integral subscript 2 superscript 4 6 x squared minus 6 x minus 1 d x equals open square brackets fraction numerator 6 over denominator 2 plus 1 end fraction x to the power of 2 plus 1 end exponent minus fraction numerator 6 over denominator 1 plus 1 end fraction x to the power of 1 plus 1 end exponent minus x close square brackets to the power of 4 subscript 2 subscript blank end subscript  space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals open square brackets 6 over 3 x cubed minus 6 over 2 x squared minus x close square brackets to the power of 4 subscript 2 subscript blank end subscript space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals open square brackets 2 x cubed minus 3 x squared minus x close square brackets to the power of 4 subscript 2 subscript blank end subscript space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals open square brackets 2 left parenthesis 4 right parenthesis cubed minus 3 left parenthesis 4 right parenthesis squared minus 4 close square brackets to the power of 4 subscript 2 subscript blank end subscript minus open square brackets 2 left parenthesis 2 right parenthesis cubed minus 3 left parenthesis 2 right parenthesis squared minus 2 close square brackets to the power of 4 subscript 2 subscript blank end subscript space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals open square brackets 2 left parenthesis 64 right parenthesis minus 3 left parenthesis 16 right parenthesis minus 4 close square brackets minus open square brackets 2 left parenthesis 8 right parenthesis minus 3 left parenthesis 4 right parenthesis minus 2 close square brackets space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals open square brackets 128 minus 48 minus 4 close square brackets minus open square brackets 16 minus 12 minus 2 close square brackets space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals open square brackets 76 close square brackets minus open square brackets 2 close square brackets space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 74 end style

 

Jadi,  begin mathsize 14px style integral subscript 2 superscript 4 6 x squared minus 6 x minus 1 d x equals 74 end style

0

Roboguru

Pembahasan Soal:

integral subscript 0 superscript 2 left parenthesis x squared minus 2 x plus 1 right parenthesis d x  rightwards double arrow left square bracket 1 third x cubed minus x squared plus x right square bracket subscript 0 superscript 2 space  equals left parenthesis 1 third left parenthesis 2 right parenthesis cubed minus 2 squared plus 2 right parenthesis minus left parenthesis 0 right parenthesis  equals left parenthesis 8 over 3 minus 4 plus 2 right parenthesis minus left parenthesis 0 right parenthesis  equals 8 over 3 minus 2 equals fraction numerator 8 minus 6 over denominator 3 end fraction equals 2 over 3

0

Roboguru

Diketahui . Nilai a yang memenuhi adalah......

Pembahasan Soal:

integral from 2 to 3 of open parentheses 3 x squared minus a x plus 5 close parentheses space d x equals negative 6 space  open x cubed minus fraction numerator a x squared over denominator 2 end fraction plus 5 x close vertical bar subscript 2 superscript 3 equals negative 6  open parentheses 27 minus fraction numerator 9 a over denominator 2 end fraction plus 15 close parentheses minus open parentheses 8 minus 2 a plus 10 close parentheses equals negative 6  24 minus fraction numerator 5 a over denominator 2 end fraction equals negative 6  fraction numerator 5 a over denominator 2 end fraction equals 30  a equals 12

0

Roboguru

Jika , maka nilai adalah...

Pembahasan Soal:

integral from 0 to 2 of xf open parentheses straight x squared close parentheses dx  Substitusi space straight y equals straight x squared comma maka  dy equals 2 xdx  box enclose 1 half dy equals straight x straight space dx end enclose  Untuk space straight x equals 0 comma space maka space straight y equals 0 squared equals 0.  Untuk space straight x equals 2 comma space maka space straight y equals 2 squared equals 4.    Sehingga  integral from 0 to 2 of xf open parentheses straight x squared close parentheses dx equals integral from 0 to 2 of straight f open parentheses straight x squared close parentheses straight space straight x space dx equals integral from 0 to 4 of straight f open parentheses straight y close parentheses open parentheses 1 half dy close parentheses equals 1 half integral from 0 to 4 of straight f open parentheses straight y close parentheses dy  equals 1 half integral from 0 to 4 of straight f open parentheses straight x close parentheses dx equals box enclose fraction numerator square root of 2 over denominator 2 end fraction end enclose

0

Roboguru

Hasil dari

Pembahasan Soal:

integral subscript 0 superscript 2 3 open parentheses x plus 1 close parentheses open parentheses x minus 6 close parentheses d x equals integral subscript 0 superscript 2 3 open parentheses x squared minus 5 x minus 6 close parentheses d x  space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 3 open parentheses 1 third x cubed minus 5 over 2 x squared minus 6 x close parentheses open table row space row space row space end table close square brackets table row 2 row space row 0 end table  space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 3 open parentheses 8 over 3 minus 10 minus 12 close parentheses  space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 3 open parentheses 8 over 3 minus 22 close parentheses  space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 8 minus 66 space space  space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals negative 58 space

0

Roboguru

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