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SIMAK UI 2010

Solusi SIMAK UI 2010 Kode 509 [IPA] – Nomor 11


Jika\ \int_1^4 f(x)\ dx=6,\ maka\ \int_1^4 f(5-x)\ dx=....
(A)\quad 6\\(B)\quad 3\\(C)\quad 0\\(D)\quad -1\\(E)\quad -6
Jawaban: A

\int_1^4 f(x)\ dx=6
Jika\ \int f(x)\ dx=F(x)\ maka\ F(4)-F(1)=6

Misalkan\ t=5-x\ maka\ dt=-dx\ sehingga\ dx=-dt
Untuk\ x=4\quad \rightarrow \quad t=1
Untuk\  x=1\quad \rightarrow \quad t=4
sehingga

\begin{array} {lcl} \int_1^4 f(5-x)\ dx&=&\int_4^1 f(t)\ (-dt)\\\\&=&-\int_4^1 f(t)\ dt\\\\&=&\int_1^4 f(t)\ dt\\\\&=&F(4)-F(1)\\\\&=&6\end{array}

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