Resolved: "∫0.22.2xexdx"

High School
Calculus and Analysis
Calculus 1
Integrals

ediculeN

Answered question

2021-09-08

$\int_{0.2}^{2.2} x e^{x} d x$

Answer & Explanation

hesgidiauE

Skilled2021-09-09Added 106 answers

Compute the definite integral:
$\int_{0.2}^{2.2} x e^{x} d x$
For the integrand $e^{x} x$ , integrate by parts, integral $f d g = f g$ - integral g df, where
$f = x, d g = e^{x} d x, d f = d x, g = e^{x}$ :
$= e^{x} x ∣_{0.2}^{2.2} - \int_{0.2}^{2.2} e^{x} d x$
Evaluate the antiderivative at the limits and subtract.
$e^{x} x ∣_{0.2}^{2.2} = e^{2.2} 2.2 - e^{0.2} 0.2 = 19.6107$ :
$= 19.6107 - \int_{0.2}^{2.2} e^{x} d x$
Apply the fundamental theorem of calculus.
The antiderivative of $e^{x}$ is $e^{x}$ :
$= 19.6107 + (- e^{x}) ∣_{0.2}^{2.2}$
Evaluate the antiderivative at the limits and subtract.
$(- e^{x}) ∣ {0.2}^{2.2} = (- e^{2.2}) - (- e^{0.2}) = - 7.80361$ :
Answer:
$= 11.8071$

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