Roboguru

Misalkan A(t) menyatakan luas daerah di bawah kurva . Jika titik P(, 0) sehingga A() : A(1) = 1 : 8 , maka perbandingan luas trapesium ABPQ:DCPQ = ....

Misalkan A(t) menyatakan luas daerah di bawah kurva begin mathsize 14px style y equals b x squared comma space space 0 less or equal than x less or equal than t end style . Jika titik P(begin mathsize 14px style x subscript 0 end style, 0) sehingga A(begin mathsize 14px style x subscript 0 end style) : A(1) = 1 : 8 , maka perbandingan luas trapesium ABPQ:DCPQ = ....

  1. 2 : 1

  2. 3 : 1

  3. 6 : 1

  4. 8 : 1

  5. 9 : 1

Jawaban:

begin mathsize 14px style straight A open parentheses straight x subscript 0 close parentheses equals integral subscript 0 superscript straight x subscript 0 end superscript space bx squared space dx  straight A open parentheses straight x subscript 0 close parentheses equals straight b over 3 straight x cubed open straight space close square brackets straight x subscript 0 over 0  straight A open parentheses straight x subscript 0 close parentheses equals straight b over 3 straight x subscript 0 superscript 3    straight A open parentheses 1 close parentheses equals integral subscript 0 superscript 1 space bx squared space dx  straight A open parentheses 1 close parentheses equals straight b over 3 straight x cubed open straight space close square brackets 1 over 0  straight A open parentheses 1 close parentheses equals straight b over 3    fraction numerator straight A open parentheses straight x subscript 0 close parentheses over denominator straight A open parentheses 1 close parentheses end fraction equals 1 over 8  fraction numerator straight b over 3 straight x subscript 0 superscript 3 over denominator straight b over 3 end fraction equals 1 over 8  straight x subscript 0 superscript 3 equals 1 over 8  straight x subscript 0 equals 1 half    Titik space straight A  straight x equals negative 1 comma space maka space straight y equals straight b open parentheses negative 1 close parentheses squared equals straight b    Titik space straight D  straight x equals 1 comma space maka space straight y equals straight b open parentheses 1 close parentheses squared equals straight b    Titik space straight Q  straight x equals 1 half comma straight space maka straight space straight y equals straight b open parentheses 1 half close parentheses squared equals 1 fourth straight b    straight L subscript ABPQ over straight L subscript DCPQ equals fraction numerator 1 half open parentheses AB plus PQ close parentheses BP over denominator 1 half open parentheses CD plus PQ close parentheses CP end fraction  straight L subscript ABPQ over straight L subscript DCPQ equals fraction numerator open parentheses straight b plus 1 fourth straight b close parentheses 3 over 2    over denominator open parentheses straight b plus 1 fourth straight b close parentheses 1 half straight space end fraction equals 3  straight L subscript ABPQ straight space colon straight space straight L subscript DCPQ equals 3 straight space colon 1 end style

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