MATERI KAMIS, 7 MARET 2024

TURUNAN FUNGSI ALJABAR

MASTAWIYAH

INTEGRAL

MASTAWIYAH

1. Integral Tak Tentu

Integral merupakan kebalikan dari turunan. Integral disebut juga sebagai antiturunan

Integral Tak tentu

Notasi Integral

Integral Tak tentu

Rumus Integral Tak Tentu

Integral Tak tentu

Contoh 1

Integral Tak tentu

Contoh 2

Integral Tak tentu

Multiple Choice

 Tentukan turunan ke-3 dari fungsi berikut ini:  

$$f\left(x\right)=3x^4-x^3+2x+5$$  

• $$72x\ -1$$  

• $$72x-6$$  

• $$72x^2-6$$  

• $$72x^2-1$$  

Multiple Choice

Tentukan integral x jika  $$f'\left(x\right)=3x^2$$  adalah...

• $$3x^3+C$$  

• $$2x^3+C$$  

• $$x^3+C$$  

• $$3x^2+C$$  

Multiple Choice

Hasil dari $$\int^{ }\left(2x+3\right)^2\ dx\ =\ ...$$  

• $$\frac{4}{3}x^3-3x^2+9x+c$$  

• $$\ \frac{4}{3}x^3+3x^2+9x\ +\ c$$  

• $$\frac{4}{3}x^3-6x^2-9x+c\$$  

• $$\frac{4}{3}x^3+6x^2+9x+c$$  

• $$\frac{3}{4}x^3+6x^2-9x+c$$  

Multiple Choice

$$\int_{ }^{ }4x^3+6x^2+10\ =...$$  

• $$x^4+3x_{ }^3+10\ +c$$  

• $$x^4+2x^3+10x\ +c$$  

• $$12x^3+12x^2+10\ +c$$  

• $$x^4+3x^3+10x+c$$  

• $$\frac{1}{4}x^4+2x^{3^{ }}+10+c$$  

Multiple Choice

Hasil dari $$\int_{ }^{ }3x^4\ dx$$ adalah

• $$4x^3+C$$  

• $$2x^4+C$$  

• $$\frac{3}{4}x^5+C$$  

• $$\frac{3}{5}x^5+C$$  

• $$-\frac{3}{5}x^5+C$$  

Contoh 3

Integral Tak Tentu

Multiple Choice

$$\int_{ }^{ }4x^3+6x^2+10\ =...$$  

• $$x^4+3x_{ }^3+10\ +c$$  

• $$x^4+2x^3+10x\ +c$$  

• $$12x^3+12x^2+10\ +c$$  

• $$x^4+3x^3+10x+c$$  

• $$\frac{1}{4}x^4+2x^{3^{ }}+10+c$$  

Multiple Choice

$$\int\left(\frac{4}{5}x^3-\ 4x^2+\frac{4}{x^2}-7\right)dx\ =\ ...$$  

• $$\frac{1}{5}x^4-\frac{4}{3}x^3-4x^{-1}-7x\ +\ c$$  

• $$\frac{1}{5}x^4-\frac{4}{3}x^3+4x^{-1}-7x+c$$  

• $$\frac{1}{5}x^4-\frac{4}{3}x^3-4x^{-1}-7+c$$  

• $$\frac{1}{5}x^4-8x^3-\frac{4}{3}x^2-7x+c$$  

• $$\frac{12}{5}x^4-8x^3-4x^{-1}-7x+c$$  

Multiple Choice

Jika  $$f\left(x\right)=4x^2-3x+2$$  , maka nilai  $$f'\left(1\right)\$$  adalah...

• 4

• 5

• 6

• 8

• 10

Multiple Choice

Turunan pertama dari $$f\left(x\right)=\left(4x^2-5\right)\left(3x+2\right)$$  adalah...

• $$f'\left(x\right)=12x^3+16x^2-15x-10$$  

• $$f'\left(x\right)=12x^3+8x^2-15x-10$$  

• $$f'\left(x\right)=36x^2+16x-15$$  

• $$f'\left(x\right)=36x^2-16x+15$$  

• $$f'\left(x\right)=36x^2+16x+15$$  

Multiple Choice

∫( 2x - 3 )( 3x + 5 ) dx =....

• 3x³ + ½ x² - 15x + C

• 3x³ - ½ x² + 15x + C

• 2x³ + ½ x² +15x + C

• 2x³ + ½ x² - 15x + C

• 2x³ - ½ x² +15x + C