# Persiapan Universitas

## Soal

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)   $$\dfrac {8}{15} \left(7\sqrt{2} + 1 \right)$$