Roboguru

∫​{cos(x+π)+tan(x+π)sec(x+π)}dx=...

Pertanyaan

integral subscript blank open curly brackets cos left parenthesis x plus straight pi right parenthesis plus space tan space left parenthesis straight x plus straight pi right parenthesis space sec space left parenthesis straight x plus straight pi right parenthesis close curly brackets space d x equals...

  1. negative sin space left parenthesis x plus straight pi right parenthesis plus space sec space left parenthesis straight x plus straight pi right parenthesis plus straight C

  2. negative sin space left parenthesis x plus straight pi right parenthesis space minus space sec space left parenthesis straight x plus straight pi right parenthesis plus straight C

  3. sin space left parenthesis x plus straight pi right parenthesis minus sec space left parenthesis straight x plus straight pi right parenthesis plus straight C

  4. sin space left parenthesis x plus straight pi right parenthesis plus space sec space left parenthesis straight x plus straight pi right parenthesis plus straight C

  5. sin space left parenthesis x minus straight pi right parenthesis space plus sec space left parenthesis straight x minus straight pi right parenthesis

Pembahasan Soal:

integral subscript blank cos space left parenthesis x plus straight pi right parenthesis plus space tan space left parenthesis straight x plus straight pi right parenthesis space sec left parenthesis straight x plus straight pi right parenthesis space dx space equals space sin space left parenthesis straight x plus straight pi right parenthesis plus space sec space left parenthesis straight x plus straight pi right parenthesis plus straight C

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

I. Roy

Mahasiswa/Alumni Universitas Negeri Surabaya

Terakhir diupdate 04 Oktober 2021

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Pertanyaan yang serupa

Pembahasan Soal:

integral open parentheses cos open parentheses 3 x minus 2 close parentheses minus 9 sin open parentheses 2 minus 3 x close parentheses close parentheses d x  equals integral cos open parentheses 3 x minus 2 close parentheses d x minus integral 9 sin open parentheses 2 minus 3 x close parentheses d x  equals 1 third sin open parentheses 3 x minus 2 close parentheses minus open parentheses negative 9 over 3 close parentheses open parentheses negative cos open parentheses 2 minus 3 x close parentheses close parentheses plus C  equals 1 third sin open parentheses 3 x minus 2 close parentheses minus 3 cos open parentheses 2 minus 3 x close parentheses plus C

0

Roboguru

∫​cos(3x+3π​)dx=....

Pembahasan Soal:

integral subscript blank cos space open parentheses 3 x plus straight pi over 3 close parentheses d x equals 1 third sin space open parentheses 3 x plus straight pi over 3 close parentheses plus C

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Roboguru

Hasil dari ∫x​sin4(3x​+2)cos(3x​+2)​dx=...

Pembahasan Soal:

Misalkanspace:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row t equals cell 3 square root of x plus 2 end cell row cell straight d t end cell equals cell 3 times 1 half times x to the power of negative 1 half end exponent straight d x end cell row cell straight d t end cell equals cell fraction numerator 3 over denominator 2 square root of x end fraction straight d x end cell row cell straight d x end cell equals cell fraction numerator 2 square root of x over denominator 3 end fraction straight d t end cell end table end style

makaundefined 

begin mathsize 14px style integral fraction numerator sin to the power of 4 space t space cos space t over denominator up diagonal strike square root of x end strike end fraction times fraction numerator 2 up diagonal strike square root of x end strike over denominator 3 end fraction straight d t equals 2 over 3 integral sin to the power of 4 space t space cos space t space straight d t end style

misalkanundefined:

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 straight d u end cell equals cell cos space t space straight d t end cell end table end style

Sehinggaundefined

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 over 3 integral sin to the power of 4 space t space cos space t space straight d t end cell equals cell 2 over 3 integral u to the power of 4 straight d u end cell row blank equals cell 2 over 3 times 1 fifth u to the power of 5 plus C end cell row blank equals cell 2 over 15 sin to the power of 5 t plus C end cell row blank equals cell 2 over 15 sin to the power of 5 open parentheses 3 square root of x plus 2 close parentheses plus C end cell end table end style

Jadi, jawaban yang tepat adalah A.

0

Roboguru

∫cos4xdx=…

Pembahasan Soal:

Ingat rumus sudut rangkap :

cos 2 x equals open curly brackets table row cell 1 minus 2 sin squared x rightwards double arrow sin squared x equals 1 half minus 1 half cos 2 x end cell row cell 2 cos squared x minus 1 rightwards double arrow cos squared x equals 1 half plus 1 half cos 2 x end cell end table close  cos to the power of 4 x  equals cos squared x. cos squared x  equals open parentheses 1 half plus 1 half cos 2 x close parentheses open parentheses 1 half plus 1 half cos 2 x close parentheses  equals 1 fourth plus 1 fourth cos 2 x plus 1 fourth cos 2 x plus 1 fourth cos squared 2 x  equals 1 fourth plus 1 half cos 2 x plus 1 fourth open parentheses 1 half plus 1 half cos 4 x close parentheses  equals 1 fourth plus 1 half cos 2 x plus 1 over 8 plus 1 over 8 cos 4 x  equals 3 over 8 plus 1 half cos 2 x plus 1 over 8 cos 4 x

Jadi,

integral cos to the power of 4 x d x equals integral open parentheses 3 over 8 plus 1 half cos 2 x plus 1 over 8 cos 4 x close parentheses d x  equals 3 over 8 x plus 1 half.1 half sin 2 x plus 1 over 8.1 fourth sin 4 x plus C  equals 3 over 8 x plus 1 fourth sin 2 x plus 1 over 32 sin 4 x plus C

0

Roboguru

∫4tan32​xsec32​xdx=…

Pembahasan Soal:

Gunakan integral subtitusi :

u equals sec 2 over 3 x  fraction numerator d u over denominator d x end fraction equals 2 over 3. sec 2 over 3 x tan 2 over 3 x  d x equals fraction numerator d u over denominator 2 over 3. sec 2 over 3 x tan 2 over 3 x end fraction

Jadi,

integral 4 tan 2 over 3 x sec 2 over 3 x d x equals integral open parentheses 4 tan 2 over 3 x sec 2 over 3 x close parentheses fraction numerator d u over denominator 2 over 3. sec 2 over 3 x tan 2 over 3 x end fraction  equals integral 4.3 over 2 d u  equals integral 6 d u  equals 6 u plus C  equals 6 sec 2 over 3 x plus C

0

Roboguru

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