Pertanyaan

∫ − 2 π 2 π ( sin 2 x − 2 ) ⋅ cos x d x = ...

$\int_{- \frac{π}{2}}^{\frac{π}{2}} (sin^{2} x - 2) \cdot cos x d x = ...$

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Klaim

S. Yoga

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

.

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

Pembahasan

Ingat bahwa: Sehingga, Misalkan: Sehingga, Jadi, .

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,

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,

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 .