What is the integral from 5 to infinity of e^{-x/4} ?

The integral from 5 to infinity of e^{-x/4} is 4/(e^{5/4)}

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integral from 5 to infinity of e^{-x/4}

\int_{5}^{\infty} e^{- \frac{x}{4}} d x

\frac{4}{e ^{\frac{5}{4}}}

Decimal

1.14601 \dots

Solution steps

\int_{5}^{\infty} e^{- \frac{x}{4}} d x

Compute the indefinite integral:

\int e^{- \frac{x}{4}} d x = - 4 e^{- \frac{x}{4}} + C

Compute the boundaries:

\int_{5}^{\infty} e^{- \frac{x}{4}} d x = 0 - (- \frac{4}{e ^{\frac{5}{4}}})

= 0 - (- \frac{4}{e ^{\frac{5}{4}}})

Simplify

= \frac{4}{e ^{\frac{5}{4}}}

\int \frac{3}{( x + 1 ) ^{2}} d x

\int 1 + x^{3} d x

t an g e n t f (x) = \frac{x ^{2}}{x - 3}

d er i v a t i v e e^{2 x} cos (3 x)

t an g e n t f (x) = 4 tan (x), at x = \frac{π}{3}

What is the integral from 5 to infinity of e^{-x/4} ?
The integral from 5 to infinity of e^{-x/4} is 4/(e^{5/4)}