Câu hỏi

Cho hàm số xácđịnh trên thỏa mãn . Biết và . Tính : A. B. C. D.

Cho hàm số  xác định trên  thỏa mãn
$f apostrophe left parenthesis x right parenthesis equals fraction numerator 1 over denominator x squared minus 1 end fraction$ . Biết  và
. Tính :
A.
B.
C.
D.

H. Anh

Giáo viên

Xác nhận câu trả lời

Giải thích

Chọn A

$f left parenthesis x right parenthesis equals integral f apostrophe left parenthesis x right parenthesis d x equals integral fraction numerator d x over denominator x squared minus 1 end fraction equals integral fraction numerator d x over denominator left parenthesis x minus 1 right parenthesis left parenthesis x plus 1 right parenthesis end fraction equals fraction numerator 1 over denominator 2 ln open vertical bar begin display style fraction numerator x minus 1 over denominator x plus 1 end fraction end style close vertical bar plus C end fraction equals open curly brackets table attributes columnalign left end attributes row cell 1 half ln fraction numerator x minus 1 over denominator x plus 1 end fraction plus C subscript 1 space k h i space x greater or equal than 1 space logical or space x less or equal than negative 1 end cell row cell 1 half ln fraction numerator 1 minus x over denominator x plus 1 end fraction plus C subscript 2 space k h i space minus 1 less or equal than x less or equal than 1 end cell end table close$
$open curly brackets table attributes columnalign left end attributes row cell table attributes columnalign left end attributes row cell f left parenthesis 3 right parenthesis plus f left parenthesis negative 3 right parenthesis equals 4 end cell end table end cell row cell table attributes columnalign left end attributes row cell f left parenthesis 1 third right parenthesis plus f left parenthesis negative 1 third right parenthesis equals 2 end cell end table end cell end table close left right double arrow open curly brackets table attributes columnalign left end attributes row cell 1 half ln 1 half plus C subscript 1 plus 1 half ln 2 plus C subscript 1 equals 4 end cell row cell 1 half ln 1 half plus C subscript 2 plus 1 half ln 2 plus C subscript 2 equals 2 end cell end table close left right double arrow open curly brackets table attributes columnalign left end attributes row cell C subscript 1 equals 2 end cell row cell C subscript 2 equals 1 end cell end table close rightwards double arrow f left parenthesis x right parenthesis equals open curly brackets table attributes columnalign left end attributes row cell 1 half ln fraction numerator x minus 1 over denominator x plus 1 end fraction plus 2 space k h i space x greater or equal than 1 logical or x less or equal than negative 1 end cell row cell 1 half ln fraction numerator 1 minus x over denominator x plus 1 end fraction plus 1 space k h i space minus 1 less or equal than x less than 1 end cell end table close$
rightwards double arrow f left parenthesis negative 5 right parenthesis plus f left parenthesis 0 right parenthesis plus f left parenthesis 2 right parenthesis equals space 1 half ln 1 half plus 5 equals 5 minus 1 half ln 2
Chọn A