Minta bantuannya dong, nomor 6, 11, 12. dimohon bantuannya.... Question from @kykzilla

October 2018 1 19 Report

Minta bantuannya dong, nomor 6, 11, 12. dimohon bantuannya...

whongaliem 6.a) $\int\limits { \frac{2}{3} x^{3} + \frac{1}{4 x^{3} } } \, dx$ = $\int\limits { \frac{2}{3} x^{3} + \frac{1}{4} x^{-3} } \, dx$
= $\frac{2}{12}$ $x^{4}$ - $\frac{1}{8}$ $x^{-2}$
= $\frac{1}{6} x^{4}$ - $\frac{1}{ 8x^{2} }$ + c
b) $\int\limits {3 - \frac{2}{ x^{2}} } + \frac{6}{ x^{3} } } \, dx$ = $\int\limits{3 - 2x^{-2} + 6x^{-3} } \, dx$
= 3x + $2x^{-1}$ - $3x^{- 2}$ + c
= 3x + $\frac{2}{x}$ - $\frac{3}{ x^{2} }$ + c
c) $\int\limits {2 + \frac{1}{ x^{2} } - \frac{3}{ x^{4} } } \, dx$ = $\int\limits {2 - x^{- 2} + 3x^{-4} } \, dx$
= 2x + $x^{- 1}$ - $x^{- 3}$ + c
= 2x + $\frac{1}{x}$ - $\frac{1}{ x^{3} }$ + c
11.a) $\int\limits { 3x^{2} + 4x + 5} \, dx$ = x³ + 2x² + 5x + c
b) $\int\limits { 10x^{4} + 3x^{2} } \, dx$ = $2x^{5}$ + x³ + c
c) $\int\limits {(x - 2)(x + 2)} \, dx$ = $\int\limits { x^{2} - 4} \, dx$
= $\frac{1}{3} x^{3}$ - 4x + c
d) $\int\limits {x (x + 1)(x - 2)} \, dx$ = $\int\limits { x^{3} - x^{2} - 2x} \, dx$
= $\frac{1}{4}x ^{4}$ - $\frac{1}{3} x^{3}$ + x² + c
12.a) F(x) = $\int\limits {f'(x)} \, dx$
= $\int\limits {2x} \, dx$
= x² + c
F(4) = 4² + c
10 = 16 + c
c = 10 - 16
c = - 6
jadi , F(x) = x² - 6
b) F(x) = $\int\limits {f'(x)} \, dx$
= $\int\limits {3( x^{2} -3)} \, dx$
= $\int\limits { 3x^{2} - 9} \, dx$
= x³ - 9x + c
F(1) = 1³ - 9 . 1 + c
12 = 1 - 9 + c
12 = - 8 + c
c = 12 + 8
c = 20
jadi, F(x) = x³ - 9x + 20

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