Mencari hasil integral: Jadi, hasil dari .

Hasil dari

Pertanyaan

Hasil dari $integral subscript 2 superscript 3 3 x squared plus 6 x plus 4 space d x equals space...$

Pembahasan Soal:

Mencari hasil integral:

$integral subscript 2 superscript 3 3 x squared plus 6 x plus 4 straight d x equals integral subscript 2 superscript 3 3 x squared straight d x plus integral subscript 2 superscript 3 6 x straight d x plus integral subscript 2 superscript 3 4 straight d x equals 3 times integral subscript 2 superscript 3 x squared straight d x plus 6 times integral subscript 2 superscript 3 x straight d x plus integral subscript 2 superscript 3 4 straight d x equals 3 open square brackets fraction numerator x to the power of 2 plus 1 end exponent over denominator 2 plus 1 end fraction close square brackets subscript 2 superscript 3 plus 6 open square brackets fraction numerator x to the power of 1 plus 1 end exponent over denominator 1 plus 1 end fraction close square brackets subscript 2 superscript 3 plus open square brackets 4 x close square brackets subscript 2 superscript 3 equals 3 open square brackets x cubed over 3 close square brackets subscript 2 superscript 3 plus 6 open square brackets x squared over 2 close square brackets subscript 2 superscript 3 plus open square brackets 4 x close square brackets subscript 2 superscript 3 equals 3 times 19 over 3 plus 6 times 5 over 2 plus 4 equals 19 plus 15 plus 4 equals 38$

Jadi, hasil dari $integral subscript 2 superscript 3 3 x squared plus 6 x plus 4 straight d x equals 38$ .

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

S. Yoga

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Terakhir diupdate 05 Juni 2021

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$2 sin A cos B equals sin open parentheses A plus B close parentheses plus sin open parentheses A minus B close parentheses 4 sin 7 x cos 3 x equals 2 open parentheses 2 sin 7 x cos 3 x close parentheses equals 2 open parentheses sin open parentheses 7 x plus 3 x close parentheses plus sin open parentheses 7 x minus 3 x close parentheses close parentheses equals 2 sin 10 x plus 2 sin 4 x$

Jadi,

$integral subscript 0 superscript 1 over 6 pi end superscript 4 sin 7 x. cos 3 x space d x equals integral subscript 0 superscript 1 over 6 pi end superscript open parentheses 2 sin 10 x plus 2 sin 4 x close parentheses space d x equals negative 2 over 10 cos 10 x minus 2 over 4 cos 4 x open table row cell 1 over 6 pi end cell row 0 end table close square brackets equals negative 1 fifth cos 10 x minus 1 half cos 4 x open table row cell 1 over 6 pi end cell row 0 end table close square brackets equals negative 1 fifth cos 10 open parentheses 1 over 6 pi close parentheses minus 1 half cos 4 open parentheses 1 over 6 pi close parentheses minus open parentheses negative 1 fifth cos 10 open parentheses 0 close parentheses minus 1 half cos 4 open parentheses 1 over 6 pi close parentheses close parentheses equals negative 1 fifth open parentheses 1 half close parentheses minus 1 half open parentheses negative 1 half close parentheses minus open parentheses negative 1 fifth open parentheses 1 close parentheses minus 1 half open parentheses 1 close parentheses close parentheses equals negative 1 over 10 plus 1 fourth plus 1 fifth plus 1 half equals 17 over 20$

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Nilai dari

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Diketahui . Nilai dari adalah...

Pembahasan Soal:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral subscript straight a superscript 3 open parentheses 3 straight x squared plus 2 straight x plus 1 close parentheses d straight x end cell equals 25 row blank rightwards double arrow cell right enclose straight x cubed plus straight x squared plus straight x end enclose subscript straight a superscript 3 equals 25 end cell row blank rightwards double arrow cell open parentheses 3 cubed plus 3 squared plus 3 close parentheses minus open parentheses straight a cubed plus straight a squared plus straight a close parentheses equals 25 end cell row blank rightwards double arrow cell 39 minus straight a cubed minus straight a squared minus straight a equals 25 end cell row blank rightwards double arrow cell straight a cubed plus straight a squared plus straight a minus 14 equals 0 end cell row blank left right double arrow cell open parentheses straight a minus 2 close parentheses open parentheses straight a squared plus straight a minus 14 close parentheses equals 0 end cell end table end style$

Nilai $begin mathsize 14px style text a end text end style$ yang memenuhi adalah:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight a minus 2 end cell equals 0 row straight a equals 2 end table end style$

Sehingga, nilai dari $begin mathsize 14px style 3 a equals 3 cross times 2 equals 6 end style$ .

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