Math Problem Statement

The image contains a series of integral and definite integral problems written in Indonesian, covering topics such as finding integrals and calculating definite integrals with given limits.

Solution

The image contains a series of integral and definite integral problems written in Indonesian. Here’s a breakdown of the problems:

1. Tentukan hasil integral dari (Find the integral result of):

a. (4x+2)dx\int (4x + 2) \, dx
b. (12x2+4x2)dx\int (12x^2 + 4x - 2) \, dx

2. Tentukan hasil integral dari (Find the integral result of):

a. (6x2+3x)dx\int (6x^2 + 3x) \, dx
b. (3x28x+4)dx\int (3x^2 - 8x + 4) \, dx

3. Tentukan nilai dari (Find the value of):

a. 12(12x2+4x)dx\int_1^2 (12x^2 + 4x) \, dx
b. 03(6x2+4x+3)dx\int_0^3 (6x^2 + 4x + 3) \, dx

4. Tentukan nilai dari (Find the value of):

a. 13(4x3+6x2+4x+2)dx\int_1^3 (4x^3 + 6x^2 + 4x + 2) \, dx
b. 12(3x2+2x+5)dx\int_{-1}^2 (3x^2 + 2x + 5) \, dx

5. Hitunglah nilai dari (Calculate the value of):

a. 03(x+3)2dx\int_0^3 (x + 3)^2 \, dx
b. 12(x+2)(x4)dx\int_1^2 (x + 2)(x - 4) \, dx

6. Hitunglah nilai dari (Calculate the value of):

a. 12(x+5)2dx\int_1^2 (x + 5)^2 \, dx
b. 12(x3)2dx\int_1^2 (x - 3)^2 \, dx

7. Hitunglah nilai dari (Calculate the value of):

a. 02(12x+3)dx\int_0^2 \left(\frac{1}{2}x + 3\right) \, dx
b. 12(14x3+2)dx\int_1^2 \left(\frac{1}{4}x^3 + 2\right) \, dx

8. Hitunglah nilai dari (Calculate the value of):

a. 12(6x2+3x+2)dx\int_1^2 (6x^2 + 3x + 2) \, dx
b. 13(3x2+4x+5)dx\int_1^3 (3x^2 + 4x + 5) \, dx


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Math Problem Analysis

Mathematical Concepts

Integral Calculus
Definite Integrals
Polynomial Integration

Formulas

∫ ax^n dx = (a/(n+1))x^(n+1) + C
Definite integrals: ∫_a^b f(x) dx

Theorems

Fundamental Theorem of Calculus

Suitable Grade Level

Undergraduate Calculus or High School Calculus