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Jan Meyer
2026-04-25 18:04:39 +02:00
parent 3421d8160d
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11 Homework/Mathe II/Homework 1.pdf
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11 Homework/Mathe II/Homework 1.typ
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@@ -1,29 +1,33 @@
#let assignment_header(course, index) = { #set page(
set page(
header: align(right, [ header: align(right, [
#set text(size: 9pt) #set text(size: 9pt)
#set par(leading: .3em) #set par(leading: .3em)
#pad(y: -.5cm, [ #pad(y: -.5cm, [
#course \ Mathe II \
Hausaufgabe #index \ Hausaufgabe 01 \
Jan Meyer \ Jan Meyer \
664237 664237
]) ])
]) ])
) )
}
#assignment_header("Mathe II", 1)
== Problem 1 _Stammfunktionen_ == Problem 1 _Stammfunktionen_
a) a) $ &integral x^2 exp(x^3) d x = 1/3 exp(x^3) + C $
$ integral x^2 exp(x^3) d x = 1/3 exp(x^3) + C $
b) b)
$ integral ln(x^2)/x^2 d x = -(2 ln(x) + 2)/x + C $ $ &integral ln(x^2)/x^2 d x = -(2 ln(x) + 2)/x + C $
c) c)
$ integral 1/2 (sin(2x) + 1) d x = 1/4 (-cos(2x) + 2x) + C $ $ &integral 1/2 (sin(2x) + 1) d x = 1/4 (-cos(2x) + 2x) + C $
== Problem 2 _Integrale und Stammfuntionen_ == Problem 2 _Integrale und Stammfuntionen_
a) a)
$ integral (2x^2 - 3x + 4) / x d x = x^2 - 3x + 4 ln abs(x) $ $ &integral (2x^2 - 3x + 4) / x d x = x^2 - 3x + 4 ln abs(x) + C $
b)
$ &integral (2 cos(x)) / (1 + sin(x)) d x = 2 ln abs(1 + sin(x)) + C $
c)
$ &integral exp(2x) sqrt(1 + exp(2x)) d x = 1/3(1 + exp(2x))^(3/2) + C $