-
Title: Integration by Parts
-
Series: Real Analysis
-
Chapter: Riemann Integral
-
YouTube-Title: Real Analysis 58 | Integration by Parts
-
Bright video: https://youtu.be/2EH3XnaDPKU
-
Dark video: https://youtu.be/5g0QKwT8CPE
-
Ad-free video: Watch Vimeo video
-
Quiz: Test your knowledge
-
Dark-PDF: Download PDF version of the dark video
-
Print-PDF: Download printable PDF version
-
Thumbnail (bright): Download PNG
-
Thumbnail (dark): Download PNG
-
Subtitle on GitHub: ra58_sub_eng.srt missing
-
Timestamps (n/a)
-
Subtitle in English (n/a)
-
Quiz Content
Q1: Let $f,g: \mathbb{R} \rightarrow \mathbb{R}$ be two continuously differentiable functions. What is the correct integration by parts rule?
A1: $\int_a^b f^\prime(x) g(x) dx = \int_a^b g(x) f^\prime(x) dx$
A2: $\int_a^b f^\prime(x) g(x) dx = f(x) g(x)|_a^b - \int_a^b g(x) f^\prime(x) dx$
A3: $\int_a^b f^\prime(x) g(x) dx = f(x) g(x)|_a^b - \int_a^b f(x) g^\prime(x) dx$
A4: $\int_a^b f^\prime(x) g(x) dx = f(x) g(x)|_a^b + \int_a^b f^\prime(x) g(x) dx$
A5: $\int_a^b f^\prime(x) g(x) dx = f^\prime(x) g(x)|_a^b - \int_a^b f^\prime(x) g(x) dx$
Q2: What is an antiderivative of the function $f:\mathbb{R} \rightarrow \mathbb{R}$ given by $$f(t) = t \sin(t)$$
A1: $$ -t \cos(t) - \sin(t) $$
A2: $$ -t \cos(t) + \sin(t) $$
A3: $$ t \cos(t) - \sin(t) $$
A4: $$ -t \cos(t) + \sin(t) $$
Q3: What is the integral $\int_0^1 t \exp(t) , dt$?
A1: $0$
A2: $\frac{1}{2} e - 1$
A3: $1$
A4: $\frac{1}{2}$
A5: $e$
-
Last update: 2024-10
