Roboguru

∫−22​(3x2+4)dx=....

Pertanyaan

integral subscript negative 2 end subscript superscript 2 left parenthesis 3 x squared plus 4 right parenthesis d x equals....

  1. 52

  2. 32

  3. 24

  4. 12

  5. 0

Pembahasan Soal:

integral subscript a superscript b a x to the power of n d x equals open square brackets fraction numerator a over denominator n plus 1 end fraction x to the power of n plus 1 end exponent close square brackets subscript a superscript b equals open parentheses fraction numerator a over denominator n plus 1 end fraction b to the power of n plus 1 end exponent close parentheses minus open parentheses fraction numerator a over denominator n plus 1 end fraction a to the power of n plus 1 end exponent close parentheses  integral subscript negative 2 end subscript superscript 2 left parenthesis 3 x squared plus 4 right parenthesis d x equals open square brackets x cubed plus 4 x close square brackets subscript negative 2 end subscript superscript 2  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 left parenthesis left parenthesis 2 right parenthesis cubed plus 4 left parenthesis 2 right parenthesis right parenthesis minus left parenthesis left parenthesis negative 2 right parenthesis cubed plus 4 left parenthesis negative 2 right parenthesis right parenthesis  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 left parenthesis 16 right parenthesis minus left parenthesis negative 16 right parenthesis  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 32

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

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Terakhir diupdate 05 Oktober 2021

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Pertanyaan yang serupa

Hasil integral ∫27​(3x−2)dx adalah ....

Pembahasan Soal:

Ingat kembali konsep Integral Tentu  sebagai berikut:

integral subscript a superscript b f open parentheses x close parentheses d x equals right enclose F open parentheses x close parentheses end enclose subscript a superscript b equals F open parentheses b close parentheses minus F open parentheses a close parentheses

Oleh karena itu, Hasil integral integral subscript 2 superscript 7 open parentheses 3 x minus 2 close parentheses d x adalah

table attributes columnalign right center left columnspacing 0px end attributes row cell integral subscript 2 superscript 7 open parentheses 3 x minus 2 close parentheses d x end cell equals cell right enclose fraction numerator 3 over denominator 1 plus 1 end fraction x to the power of 1 plus 1 end exponent minus 2 x end enclose subscript 2 superscript 7 end cell row blank equals cell right enclose 3 over 2 x squared minus 2 x end enclose subscript 2 superscript 7 end cell row blank equals cell open parentheses 3 over 2 open parentheses 7 close parentheses squared minus 2 open parentheses 7 close parentheses close parentheses minus open parentheses 3 over 2 open parentheses 2 close parentheses squared minus 2 open parentheses 2 close parentheses close parentheses end cell row blank equals cell open parentheses 73 comma 5 minus 14 close parentheses minus open parentheses 6 minus 4 close parentheses end cell row blank equals cell 59.5 minus 2 end cell row blank equals cell 57 comma 5 end cell row blank blank blank end table

Dengan demikian, Hasil integral integral subscript 2 superscript 7 open parentheses 3 x minus 2 close parentheses d x adalah 57 comma 5.

0

Roboguru

Nilai a yang memenuhi ∫1a​(2x+3)dx=6 adalah …

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 1 superscript a open parentheses 2 x plus 3 close parentheses d x end cell equals cell right enclose x squared plus 3 x end enclose subscript 1 superscript a end cell row 6 equals cell open parentheses a squared plus 3 a close parentheses minus open parentheses open parentheses 1 close parentheses squared plus 3 open parentheses 1 close parentheses close parentheses end cell row 6 equals cell a squared plus 3 a minus open parentheses 1 plus 3 close parentheses end cell row 6 equals cell a squared plus 3 a minus 4 end cell row 0 equals cell a squared plus 3 a minus 10 end cell row 0 equals cell open parentheses a plus 5 close parentheses open parentheses a minus 2 close parentheses end cell end table

sehingga diperoleh

table row cell a plus 5 equals 0 end cell atau cell a minus 2 equals 0 end cell row cell a equals negative 5 end cell blank cell a equals 2 end cell end table

Jadi, nilai a yang memenuhi integral subscript 1 superscript a open parentheses 2 x plus 3 close parentheses d x equals 6 adalah negative sign 5 space atau space 2.

0

Roboguru

Nilai dari ∫−11​(4x2−3x−10)dx adalah...

Pembahasan Soal:

begin mathsize 14px style integral subscript negative 1 end subscript superscript 1 left parenthesis 4 x squared minus 3 x minus 10 right parenthesis d x equals right enclose 4 over 3 x cubed minus 3 over 2 x squared minus 10 x end enclose subscript negative 1 end subscript superscript 1 equals open parentheses 4 over 3 times 1 cubed minus 3 over 2 times 1 squared minus 10 times 1 close parentheses minus open parentheses 4 over 3 times open parentheses negative 1 close parentheses cubed minus 3 over 2 times open parentheses negative 1 close parentheses squared minus 10 times open parentheses negative 1 close parentheses close parentheses equals open parentheses 4 over 3 minus 3 over 2 minus 10 close parentheses minus open parentheses negative 4 over 3 minus 3 over 2 plus 10 close parentheses equals 4 over 3 plus 4 over 3 minus 3 over 2 plus 3 over 2 minus 10 minus 10 equals 8 over 3 minus 20 equals negative 17 1 third end style

Dengan demikian nilai dari begin mathsize 14px style integral subscript negative 1 end subscript superscript 1 open parentheses 4 x squared minus 3 x minus 10 close parentheses d x equals negative 17 1 third end style.

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Roboguru

∫−12​(5x+1)(3x+5)dx=....

Pembahasan Soal:

integral subscript negative 1 end subscript superscript 2 open parentheses 5 x plus 1 close parentheses open parentheses 3 x plus 5 close parentheses d x  equals integral subscript negative 1 end subscript superscript 2 open parentheses 15 x squared plus 28 x plus 5 close parentheses d x  equals 5 x plus 14 x squared plus 5 x subscript negative 1 end subscript superscript 2  equals 102

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Roboguru

∫02​x2dx=

Pembahasan Soal:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral subscript 0 superscript 2 x squared space d x end cell equals cell open square brackets 1 third x cubed close square brackets subscript 0 superscript 2 end cell row blank equals cell 1 third left parenthesis 2 right parenthesis cubed minus fraction numerator 1 over denominator 3 end fraction open parentheses 0 close parentheses cubed end cell row blank equals cell 8 over 3 minus 0 end cell row blank equals cell 2 2 over 3 end cell end table end style 

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