8.4.1 Final Test Module <a href="#VBKM08">1.8</a>

Chapter 8 Integral Calculus

Section 8.4 Final Test

8.4.1 Final Test Module 1.8

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Exercise 8.4.1

Find an antiderivative for each of the following functions:

$\int 3 \sqrt{x} d x =$
$\int (2 x - e^{x + π}) d x =$

iExpInputHint

Exercise 8.4.2

Calculate the integrals

\int_{1}^{e} \frac{1}{2 x} d x =

and

\int_{5}^{8} \frac{6}{x - 4} d x =

Exercise 8.4.3

Calculate the integrals

\int_{0}^{3} x \cdot \sqrt{x + 1} d x =

and

\int_{π}^{\frac{3 π}{4}} 5 \sin (4 x - 3 π) d x =

Exercise 8.4.4

Fill in the boxes.

2 \int_{a}^{4} | x^{3} | d x = \int_{- 4}^{4} | x^{3} | d x

| \int_{- 4}^{4} x^{3} d x |

for

a =

.
Fill in the boxes such that the statement is correct. Enter comparators as =, <= or >=.

Exercise 8.4.5

Calculate the area

I_{A}

of the region

A

that is bounded by the graphs of the two functions

f

and

g

[- 3; 2]

with

f (x) = x^{2}

and

g (x) = 6 - x

.
Answer:

I_{A} =

Exercise 8.4.6

Let an antiderivative

F

of the function

f

and an antiderivative

G

of the function

g

be given. Moreover, the function

id

with

id (x) = x

is given.
Which of the following statements are always true (provided the corresponding combinations/compositions are possible)?

True?	Statement:
	$id \cdot F$ is an antiderivative of $id \cdot f$
	$F \circ G$ is an antiderivative of $f \circ g$
	$F - G$ is an antiderivative of $f - g$
	$F / G$ is an antiderivative of $f / g$
	$F \cdot G$ is an antiderivative of $f \cdot g$
	$- 20 \cdot F$ is an antiderivative of $- 20 \cdot f$

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1. Elementary Arithmetic

2. Equations in one Variable

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4. System of Linear Equations

5. Geometry

6. Elementary Functions

7. Differential Calculus

8. Integral Calculus

9. Objects in the Two-Dimensional Coordinate System

10. Basic Concepts of Descriptive Vector Geometry

11. Language of Descriptive Statistics