carilah anti turunan F(x) + C bila a. f(x) = 3x^2-10x+5 b. f(x) = x^2 (20x^7- 7x^5+6) c. f(x) = 1/x^3 +6/x^7

Posted by andi telaumbanua on Jul 28, 2018 in Matematika |
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carilah anti turunan F(x) + C bila

a. f(x) = 3x^2-10x+5
b. f(x) = x^2 (20x^7- 7x^5+6)
c. f(x) = 1/x^3 +6/x^7

Jawab:

∫f(x)dx = F(x)+ C

Maka:

a. f(x) = 3x^2-10x+5 anti turunannya adalah

∫ (3x^2-10x+5)dx = 3/3 x^3-10/2 x^2+5x+ C

= x^3-5x^2+5x+C

b. f(x) = x^2 (20x^7- 7x^5+6) anti turunannya adalah

∫ x^2 (20x^7- 7x^5+6) dx = ∫ (20x^9- 7x^7+6x^2 ) dx

= 20/10 x^10-7/8 x^8+6/3 x^3+ C

= 2 x^10-7/8 x^8+ 2x^3+ C

c. f(x) = 1/x^3 +6/x^7 anti turunannya adalah

∫ (1/x^3 +6/x^7 )dx = -1/2 x^(-2)-6/6 x^(-6)

=-1/(2x^2 )-1/x^6

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