What is the integral from 1.2 to 5.4 of 1.6xe^{x/3} ?

The integral from 1.2 to 5.4 of 1.6xe^{x/3} is 82.58130…

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integral from 1.2 to 5.4 of 1.6xe^{x/3}

\int_{1.2}^{5.4} 1.6 x e^{\frac{x}{3}} d x

82.58130 \dots

Solution steps

\int_{1.2}^{5.4} 1.6 x e^{\frac{x}{3}} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 1.6 \cdot \int_{1.2}^{5.4} x e^{\frac{x}{3}} d x

Apply Integration By Parts

: [3 e^{\frac{x}{3}} x - \int 3 e^{\frac{x}{3}} d x]_{1.2}^{5.4}

= 1.6 [3 e^{\frac{x}{3}} x - \int 3 e^{\frac{x}{3}} d x]_{1.2}^{5.4}

\int 3 e^{\frac{x}{3}} d x = 9 e^{\frac{x}{3}}

= 1.6 [3 e^{\frac{x}{3}} x - 9 e^{\frac{x}{3}}]_{1.2}^{5.4}

Compute the boundaries:

51.61331 \dots

= 1.6 \cdot 51.61331 \dots

Simplify

= 82.58130 \dots

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What is the integral from 1.2 to 5.4 of 1.6xe^{x/3} ?
The integral from 1.2 to 5.4 of 1.6xe^{x/3} is 82.58130…