Soal 01
SIMAK UI 2019 Matematika IPA Kode 331
Jika \(\displaystyle \int_a^b f'(x) f(x) \: dx = 10\) dan \(f(a) = 2 + f(b)\), nilai \(f(b)\) adalah ...
(A) −2
(B) −4
(C) −6
(D) −8
(E) −10
Soal 02
SIMAK UI 2018 Matematika IPA Kode 412
Jika \(f(x)\) fungsi kontinu di interval [1,30] dan \(\displaystyle \int_{6}^{30} f(x) \: dx = 30\) maka \(\displaystyle \int_{1}^{9} f(3y + 3) \: dy = \dotso\)
(A) 5
(B) 10
(C) 15
(D) 18
(E) 27
Soal 03
SIMAK UI 2017 Matematika IPA Kode 341
Jika \(\displaystyle 3x^5 - 3 = \int_c^x g(t) \: dt\), maka \(g \left(\dfrac c2 \right) = \dotso\)
(A) \(\dfrac {10}{16}\)
(B) \(\dfrac {12}{16}\)
(C) \(\dfrac {14}{16}\)
(D) \(\dfrac {15}{16}\)
(E) \(\dfrac {17}{16}\)
Soal 04
SIMAK UI 2017 Matematika IPA Kode 341
Jika \(f(x) = \frac 13 x^3 - 2x^2 + 3x\) dengan \(-1 \leq x \leq 2\) mempunyai titik maksimum di \((a,b)\), maka nilai \(\displaystyle \int_a^b f'(x) \: dx\) adalah ...
(A) \(\dfrac {16}{81}\)
(B) \(\dfrac {15}{81}\)
(C) \(\dfrac {12}{81}\)
(D) \(\dfrac {9}{81}\)
(E) \(\dfrac {8}{81}\)
Soal 05
SIMAK UI 2015 Internasional Matematika IPA Kode 111
A function has slope function \(y = 2 \sqrt{x} + \dfrac {a}{\sqrt{x}}\) and passes through the points \((0,2)\) and \((1,4)\). The value of a is ...
(A) \(\dfrac {1}{3}\)
(B) \(\dfrac {2}{3}\)
(C) \(\dfrac {4}{3}\)
(D) \(\dfrac {1}{2}\)
(E) \(\dfrac {3}{2}\)
Soal 06
SIMAK UI 2014 Matematika IPA Kode 301
Diberikan fungsi \(f\) dan \(g\) yang memenuhi sistem
\(\displaystyle \int_0^1 f(x) \: dx + \left(\int_0^2 g(x) \: dx \right)^2 = 3\)
\(\displaystyle f(x) = 3x^2 + 4x + \int_0^2 g(x) \: dx\)
dengan \(\displaystyle \int_0^2 g(x) \: dx \neq 0\).
Nilai \(f(1) = \dotso\)
(A) −6
(B) −3
(C) 0
(D) 3
(E) 6
Soal 07
SIMAK UI 2014 Matematika IPA Kode 302
Jika \(\displaystyle \int_{-1}^a \dfrac {x + 1}{(x + 2)^4} \: dx = \dfrac {10}{81}\) dan \(a > -2\), maka \(a = \dotso\)
(A) \(- 1 \dfrac 12\)
(A) \(- 1\)
(C) \(0\)
(D) \(1\)
(E) \(1 \dfrac 12\)
Soal 08
SIMAK UI 2013 Matematika IPA Kode 132
Jika \(\displaystyle \int_{0}^2 \dfrac {x^2 + 3x}{\sqrt{x + 2}} \: dx = \dotso\)
(A) \(\dfrac {4}{15} \left(7 - \sqrt{2}\right)\)
(A) \(\dfrac {4}{15} \left(7\sqrt{2} - 1\right)\)
(C) \(\dfrac {4}{15} \left(7\sqrt{2} + 1\right)\)
(D) \(\dfrac {8}{15} \left(7\sqrt{2} - 1\right)\)
(E) \(\dfrac {8}{15} \left(7\sqrt{2} + 1 \right)\)