What is the integral from 2 to 6 of 0.35e^{-0.35x} ?

The integral from 2 to 6 of 0.35e^{-0.35x} is 0.37412…

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integral from 2 to 6 of 0.35e^{-0.35x}

\int_{2}^{6} 0.35 e^{- 0.35 x} d x

0.37412 \dots

Solution steps

\int_{2}^{6} 0.35 e^{- 0.35 x} d x

Take the constant out:

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

= 0.35 \cdot \int_{2}^{6} e^{- 0.35 x} d x

Apply u-substitution

= 0.35 \cdot \int_{- 0.7}^{- 2.1} - \frac{1}{0.35} e^{u} d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= 0.35 (- \int_{- 2.1}^{- 0.7} - \frac{1}{0.35} e^{u} d u)

Take the constant out:

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

= 0.35 (- (- \frac{1}{0.35} \cdot \int_{- 2.1}^{- 0.7} e^{u} d u))

Simplify

= 0.35 (- (- 2.85714 \dots \cdot \int_{- 2.1}^{- 0.7} e^{u} d u))

Use the common integral:

\int e^{u} d u = e^{u}

= 0.35 (- (- 2.85714 \dots [e^{u}]_{- 2.1}^{- 0.7}))

Simplify

= [e^{u}]_{- 2.1}^{- 0.7}

Compute the boundaries:

0.37412 \dots

= 0.37412 \dots

What is the integral from 2 to 6 of 0.35e^{-0.35x} ?
The integral from 2 to 6 of 0.35e^{-0.35x} is 0.37412…