How do you evaluate the definite integral $(x^{43}) e^{- x^{44}} d x$ $(x^43)e^(-x^(44)) dx$ for a=0, b=1?

Question

How do you evaluate the definite integral $(x^{43}) e^{- x^{44}} d x$ $(x^43)e^(-x^(44)) dx$ for a=0, b=1?

1 Answer

Impact of this question

4089 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-05-24T22:11:49

We have to look for a primitive of the function $f (x) = x^{43} e^{- x^{44}}$ $f(x)=x^43e^{-x^44}$

For the chain rule,

$\frac{d}{d x} (e^{- x^{44}}) = e^{- x^{44}} (- 44 x^{43})$ $d/dx(e^{-x^44})=e^{-x^44}(-44x^43)$

So we have a primitive for $f$ $f$ (we just have to divide by $- 44$ $-44$ ), and we have, for the fundamental theorem of integral calculus:

$\int_{0}^{1} x^{43} e^{- x^{44}} = \frac{e^{- x^{44}}}{- 44} {∣ ∣ ∣}_{0}^{1}$ $int_0^1x^43e^{-x^44}=e^{-x^44}/(-44)|_0^1$ $= - \frac{1}{44 e} + \frac{1}{44}$ $=-1/(44e)+1/44$

Science

Math

Humanities

... and beyond

How do you evaluate the definite integral $(x^{43}) e^{- x^{44}} d x$ $(x^43)e^(-x^(44)) dx$ for a=0, b=1?

1 Answer

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you evaluate the definite integral (x43)e−x44dx(x^43)e^(-x^(44)) dx for a=0, b=1?

1 Answer

Related questions

Impact of this question

How do you evaluate the definite integral $(x^{43}) e^{- x^{44}} d x$ $(x^43)e^(-x^(44)) dx$ for a=0, b=1?