{\int_{{{0.2}}}^{{{2.2}}}}{x}{e}^{x}{\left.{d}{x}\right.}

ediculeN

ediculeN

Answered question

2021-09-08

0.22.2xexdx

Answer & Explanation

hesgidiauE

hesgidiauE

Skilled2021-09-09Added 106 answers

Compute the definite integral:
0.22.2xexdx
For the integrand exx, integrate by parts, integral fdg=fg - integral g df, where
f=x,dg=exdx,df=dx,g=ex:
=exx0.22.20.22.2exdx
Evaluate the antiderivative at the limits and subtract.
exx0.22.2=e2.22.2e0.20.2=19.6107:
=19.61070.22.2exdx
Apply the fundamental theorem of calculus.
The antiderivative of ex is ex:
=19.6107+(ex)0.22.2
Evaluate the antiderivative at the limits and subtract.
(ex)0.22.2=(e2.2)(e0.2)=7.80361:
Answer:
=11.8071

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