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Pertanyaan

Nilai integral subscript 1 over 6 straight pi end subscript superscript 1 third straight pi end superscript open parentheses 3 space cos space x space minus space 5 space sin space x close parentheses space straight d x equals...

  1. 4 minus 4 square root of 3

  2. negative 1 minus 3 square root of 3

  3. 1 minus square root of 3

  4. 1 plus square root of 3

  5. 4 plus 4 square root of 3

Pembahasan Soal:

Ingat! 

integral cos space x space straight d x equals space sin space x space plus C integral space sin space x space straight d x equals negative cos space x space plus C space

Mengoperasikan integral:

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell integral subscript 1 over 6 straight pi end subscript superscript 1 third straight pi end superscript open parentheses 3 space cos space x space minus space 5 space sin space x close parentheses space straight d x end cell row blank equals cell open square brackets 3 space sin space x plus 5 space cos space x close square brackets subscript 1 over 6 straight pi end subscript superscript 1 third straight pi end superscript end cell row blank equals cell open square brackets 3 space sin space straight pi over 3 plus 5 space cos space straight pi over 3 close square brackets minus open square brackets 3 space sin straight pi over 6 plus 5 space cos straight pi over 6 close square brackets end cell row blank equals cell open square brackets 3 open parentheses fraction numerator square root of 3 over denominator 2 end fraction close parentheses plus 5 open parentheses 1 half close parentheses close square brackets minus open square brackets 3 open parentheses 1 half close parentheses plus 5 open parentheses fraction numerator square root of 3 over denominator 2 end fraction close parentheses close square brackets end cell row blank equals cell fraction numerator 3 square root of 3 over denominator 2 end fraction minus fraction numerator 5 square root of 3 over denominator 2 end fraction plus 5 over 2 minus 3 over 2 end cell row blank equals cell fraction numerator negative 2 square root of 3 over denominator 2 end fraction plus 2 over 2 end cell row blank equals cell negative square root of 3 plus 1 end cell row blank equals cell 1 minus square root of 3 end cell end table

Oleh karena itu, jawaban yang benar adalah C.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

O. Rahmawati

Mahasiswa/Alumni UIN Sunan Gunung Djati Bandung

Terakhir diupdate 07 Juni 2021

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Pertanyaan yang serupa

Hasil

Pembahasan Soal:

begin mathsize 14px style integral subscript negative pi over 2 end subscript superscript pi over 2 end superscript left parenthesis sin cubed space t space cos space t right parenthesis d t equals space.... end style 

Misalkan:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row u equals cell sin space t end cell row cell fraction numerator d u over denominator d t end fraction end cell equals cell cos space t end cell row cell d u end cell equals cell cos space t space d t end cell end table end style 

Sehingga, 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral subscript negative pi over 2 end subscript superscript pi over 2 end superscript left parenthesis sin cubed space t space cos space t right parenthesis d t end cell equals cell space integral subscript negative pi over 2 end subscript superscript pi over 2 end superscript u cubed d u end cell row blank equals cell open square brackets fraction numerator u to the power of n plus 1 end exponent over denominator n plus 1 end fraction close square brackets subscript negative pi over 2 end subscript superscript pi over 2 end superscript end cell row blank equals cell open square brackets u to the power of 4 over 4 close square brackets subscript negative pi over 2 end subscript superscript pi over 2 end superscript end cell row blank equals cell open square brackets fraction numerator sin to the power of 4 t over denominator 4 end fraction close square brackets subscript negative pi over 2 end subscript superscript pi over 2 end superscript end cell row blank equals cell fraction numerator sin to the power of 4 open parentheses pi over 2 close parentheses over denominator 4 end fraction minus fraction numerator sin to the power of 4 open parentheses negative pi over 2 close parentheses over denominator 4 end fraction end cell row blank equals cell 1 fourth minus 1 fourth end cell row blank equals 0 end table end style

Roboguru

Pembahasan Soal:

Ingat bahwa:

  • table attributes columnalign right center left columnspacing 0px end attributes row cell integral f open parentheses x close parentheses plus-or-minus g open parentheses x close parentheses d x end cell equals cell integral f open parentheses x close parentheses d x plus-or-minus integral g open parentheses x close parentheses d x end cell row cell integral x to the power of a straight d x end cell equals cell fraction numerator x to the power of a plus 1 end exponent over denominator a plus 1 end fraction comma space a not equal to negative 1 end cell row cell integral a f left parenthesis x right parenthesis straight d x end cell equals cell a integral f left parenthesis x right parenthesis straight d x end cell row cell integral cos space left parenthesis x right parenthesis straight d x end cell equals cell sin space x end cell end table 

Sehingga,

table attributes columnalign right center left columnspacing 0px end attributes row cell integral subscript negative straight pi over 2 end subscript superscript straight pi over 2 end superscript open parentheses sin squared space x minus 2 close parentheses times cos space x space d x end cell equals cell integral subscript negative straight pi over 2 end subscript superscript straight pi over 2 end superscript cos open parentheses x close parentheses sin squared open parentheses x close parentheses minus cos open parentheses x close parentheses times 2 space d x end cell row blank equals cell integral subscript negative straight pi over 2 end subscript superscript straight pi over 2 end superscript open parentheses cos open parentheses x close parentheses sin squared open parentheses x close parentheses minus 2 cos open parentheses x close parentheses close parentheses space d x end cell row blank equals cell integral subscript negative pi over 2 end subscript superscript pi over 2 end superscript cos open parentheses x close parentheses sin squared open parentheses x close parentheses d x minus integral subscript negative pi over 2 end subscript superscript pi over 2 end superscript 2 cos open parentheses x close parentheses d x end cell end table 

Misalkan:

table attributes columnalign right center left columnspacing 0px end attributes row u equals cell sin open parentheses x close parentheses end cell row cell straight d u end cell equals cell cos open parentheses x close parentheses straight d x end cell row cell straight d x end cell equals cell fraction numerator 1 over denominator cos open parentheses x close parentheses end fraction straight d u end cell row blank blank blank row u equals cell sin open parentheses x close parentheses end cell row x equals cell negative pi over 2 rightwards arrow u equals negative 1 end cell row x equals cell pi over 2 rightwards arrow u equals 1 end cell end table 

Sehingga,

integral subscript negative pi over 2 end subscript superscript pi over 2 end superscript cos open parentheses x close parentheses sin squared open parentheses x close parentheses straight d x minus integral subscript negative pi over 2 end subscript superscript pi over 2 end superscript 2 cos open parentheses x close parentheses straight d x equals integral subscript negative 1 end subscript superscript 1 u squared straight d u minus 2 times integral subscript negative pi over 2 end subscript superscript pi over 2 end superscript cos open parentheses x close parentheses straight d x equals open square brackets u cubed over 3 close square brackets subscript negative 1 end subscript superscript 1 minus 2 open square brackets sin open parentheses x close parentheses close square brackets subscript negative pi over 2 end subscript superscript pi over 2 end superscript equals open square brackets 1 third minus open parentheses negative 1 third close parentheses close square brackets minus open square brackets 2 times thin space 2 close square brackets equals 2 over 3 minus 4 equals negative 10 over 3 

Jadi, integral subscript negative pi over 2 end subscript superscript pi over 2 end superscript open parentheses sin squared open parentheses x close parentheses minus 2 close parentheses cos open parentheses x close parentheses straight d x equals negative 10 over 3.

Roboguru

Pembahasan Soal:

integral open parentheses sin x plus 3 cos x close parentheses d x  equals integral sin x d x plus integral 3 cos x d x  equals negative cos x plus 3 sin x plus C

Roboguru

Hasil dari = ....

Pembahasan Soal:

begin mathsize 14px style integral open parentheses cos cubed invisible function application space 2 x. sin invisible function application space 2 x close parentheses d x space equals integral open parentheses cos cubed invisible function application space 2 x. sin invisible function application space 2 x close parentheses fraction numerator d open parentheses cos space invisible function application 2 x close parentheses over denominator negative 2 space. space sin space invisible function application 2 x end fraction  equals negative 1 half integral cos cubed invisible function application space 2 x space d space open parentheses cos space invisible function application 2 x close parentheses  equals negative 1 half open square brackets 1 fourth cos to the power of 4 invisible function application space 2 x close square brackets plus C  equals negative 1 over 8 cos to the power of 4 invisible function application space 2 x plus C end style

Roboguru

Hadil dari  adalah ...

Pembahasan Soal:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral left parenthesis 3 space sin space x plus 3 space cos space x right parenthesis space d x end cell equals cell 3 space left parenthesis negative cos space x right parenthesis plus 3 space sin space x plus C end cell row blank equals cell negative 3 space cos space x plus 3 space sin space x plus C end cell row blank equals cell 3 space sin space x minus 3 space cos space x plus C end cell end table end style 

Jadi, jawaban yang tepat adalah D

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