If $p(x)$ is a polynomial function, then $p$ has exactly one antiderivative whose graph contains the origin.
Added by Diego A.
Step 1
Step 1: Let $p(x)$ be a polynomial function, which can be written as $p(x) = a_0 + a_1x + a_2x^2 + a_3x^3 + \ldots$. Show more…
Show all steps
Close
Your feedback will help us improve your experience
Ma. Theresa Alin and 80 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
If $c$ is a zero of the polynomial $P$, then a. $P(c)=$ __________ . b. $x-c$ is a __________ $\operatorname{of} P(x)$ c. $c$ is a $(\mathrm{n})$ __________ -intercept of the graph of $P$
Polynomial and Rational Functions
Dividing Polynomials
(a) Assuming there is a function $p$ for which $\int x^{3} e^{x} d x=p(x) e^{x}$, show that $p(x)+p^{\prime}(x)=x^{3}$ (b) Use integration by parts to find a polynomial $p$ of degree 3 for which $\int x^{3} e^{x} d x=p(x) e^{x}+C$.
Techniques of Integration
Integration by Parts
True or False? In Exercises $73-78$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If $p(x)$ is a polynomial function, then $p$ has exactly one antiderivative whose graph contains the origin.
Integration
Antiderivatives and Indefinite Integration
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD