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:
  1. 3xdx=
  2. (2x-ex+π )dx=

Exercise 8.4.2
Calculate the integrals
1 e 1 2x dx=
and 5 8 6 x-4 dx=

Exercise 8.4.3
Calculate the integrals
0 3 x·x+1dx=
and π 3π 4 5sin(4x-3π)dx=

Exercise 8.4.4
Fill in the boxes.
2 a 4 | x3 |dx= -4 4 | x3 |dx  
  | -4 4 x3 dx|
for a= .
Fill in the boxes such that the statement is correct. Enter comparators as =, <= or >=.

Exercise 8.4.5
Calculate the area IA of the region A that is bounded by the graphs of the two functions f and g on [-3;2] with f(x)= x2 and g(x)=6-x.
Answer: IA =

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·F is an antiderivative of id·f
FG is an antiderivative of fg
F-G is an antiderivative of f-g
F/G is an antiderivative of f/g
F·G is an antiderivative of f·g
-20·F is an antiderivative of -20·f

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