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Tính tích phân

Tính tích phân 1 equals stretchy integral subscript 0 superscript pi over 2 end superscript   cos invisible function application 2 x open parentheses sin to the power of 4 invisible function application x plus cos to the power of 4 invisible function application x close parentheses d x

R. Roboctvx97

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Giải thích

Tính tích phân Biết d ( sin 2 x ) = ( sin 2 x ) ′ d x = 2 cos 2 x d x Do đó Cách khác Tính Suy ra I = I 1 ​ − I 2 ​ = 0

Tính tích phân table attributes columnalign right end attributes row I cell blank equals stretchy integral subscript 0 superscript pi over 2 end superscript     cos invisible function application 2 x open parentheses sin to the power of 4 invisible function application x plus cos to the power of 4 invisible function application x close parentheses d x end cell row blank cell blank equals stretchy integral subscript 0 superscript pi over 2 end superscript     cos invisible function application 2 x open parentheses 1 minus 1 half sin squared invisible function application 2 x close parentheses d x end cell end table

Biết 

Do đó I equals integral subscript 0 superscript pi over 2 end superscript   open parentheses 1 minus 1 half sin squared invisible function application 2 x close parentheses cos invisible function application 2 x d x

table attributes columnalign right end attributes row blank cell blank equals 1 half stretchy integral subscript 0 superscript pi over 2 end superscript     open parentheses 1 minus 1 half sin squared invisible function application 2 x close parentheses d left parenthesis sin invisible function application 2 x right parenthesis end cell row blank cell blank equals 1 half stretchy integral subscript 0 superscript pi over 2 end superscript     d left parenthesis sin invisible function application 2 x right parenthesis minus 1 fourth stretchy integral subscript 0 superscript pi over 2 end superscript     sin squared invisible function application 2 x d left parenthesis sin invisible function application 2 x right parenthesis end cell row blank cell blank equals open 1 half sin invisible function application 2 x close vertical bar subscript 0 superscript pi over 2 end superscript minus open 1 over 12 sin cubed invisible function application 2 x close vertical bar subscript 0 superscript pi over 2 end superscript equals 0 end cell end table

Cách khác table attributes columnalign right end attributes row I cell blank equals stretchy integral subscript 0 superscript pi over 2 end superscript     open parentheses cos squared invisible function application x minus sin squared invisible function application x close parentheses open parentheses cos to the power of 4 invisible function application x plus sin to the power of 4 invisible function application x close parentheses d x end cell row blank cell blank equals stretchy integral subscript 0 superscript pi over 2 end superscript     open parentheses cos to the power of 4 invisible function application x minus sin to the power of 4 invisible function application x close parentheses open parentheses cos to the power of 4 invisible function application x plus sin to the power of 4 invisible function application x close parentheses d x end cell end table

equals stretchy integral subscript 0 superscript n   cos to the power of x invisible function application x d x stretchy integral subscript 0 superscript pi   sin to the power of x invisible function application x d x minus I subscript 1 minus I subscript 2

Tính I equals stretchy integral subscript 0 superscript straight infinity   cos to the power of x invisible function application x d x equals stretchy integral subscript 0   sin to the power of x invisible function application open parentheses pi over 2 minus x close parentheses d x equals stretchy integral subscript 2 superscript 11   sin to the power of x invisible function application t left parenthesis negative d t right parenthesis

equals stretchy integral subscript 11 superscript 2   sin to the power of x invisible function application t d t equals 1 subscript 2

Suy ra 

 

1

Câu hỏi tương tự

Tinh a , b of cho ham s б́ f ( x ) = x 2 a ​ + x b ​ + 2 thả mãn các điều kiện f ( 2 1 ​ ) = − 4 ∫ 2 1 ​ 1 ​ f ( x ) d z = 2 − 3 in 2

4

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