In Problems 42-45, find the given quantities. The error function, erf(x), is defined by $ ext{erf}(x) = frac{2}{sqrt{pi}} int_0^x e^{-t^2} dt$. 42. $frac{d}{dx}(x ext{erf}(x))$ 44. $frac{d}{dx} left( int_0^{x^3} e^{-t^2} dt ight)$ 43. $frac{d}{dx}( ext{erf}(sqrt{x}))$ 45. $frac{d}{dx} left( int_x^{x^3} e^{-t^2} dt ight)$
Added by Tyler P.
Close
Step 1
Problem 42: ∫x*erf(x) dx Show more…
Show all steps
Your feedback will help us improve your experience
Bcrypt_Sha256$$2B$12$We1Wwocamog01O5I.V2Tkouxdh4Ofnmgpwkor7Leaonfpu0Ubfpua Bcrypt_Sha256$$2B$12$We1Wwocamog01O5I.V2Tkokttmmj7Lscvwvlptp4Rlhbswcdg9.Wy and 91 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
The error function, or erf, is defined as: erf(x) = (2 / √π) ∫ e^(-t^2) dt The error function cannot be written in terms of elementary functions; this is the simplest way to write it. Fill in the blanks to compute the following integral: ∫ 4x erf(x) dx = ( ) erf(x) + [ ] + C.
Pakkiri K.
Find the given quantities. The error function, erf $(x),$ is defined by \[\operatorname{erf}(x)=\frac{2}{\sqrt{\pi}} \int_{0}^{x} e^{-t^{2}} d t.\] $$\frac{d}{d x}(x \operatorname{erf}(x))$$
Constructing Antiderivatives
Second Fundamental Theorem of Calculus
Find the given quantities. The error function, erf $(x),$ is defined by \[\operatorname{erf}(x)=\frac{2}{\sqrt{\pi}} \int_{0}^{x} e^{-t^{2}} d t.\] $$\frac{d}{d x}(\operatorname{erf}(\sqrt{x}))$$
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