Step by step solution to "Evaluate the integral. ∫−205−0d0"

Wribreeminsl

Answered question

2021-11-06

Evaluate the integral.

\int_{- 2}^{0} 5^{- 0} d 0

broliY

Skilled2021-11-07Added 97 answers

\int_{- 2}^{0} 5^{- 0} d 0

Now, using the formula of integration as,

\int a^{x} d x = \frac{a^{x}}{\log a} + c

to integrate the given integral.

\int_{- 2}^{0} 5^{- 0} d 0 = - {[\frac{5^{- 0}}{\log (5)}]}_{- 2}^{0}

= - {[\frac{1}{5^{0} \log (5)}]}_{- 2}^{0}

= - \frac{1}{5^{0} \log (5)} + \frac{1}{5^{- 2} \log (5)}

= - \frac{1}{\log (5)} + \frac{25}{\log (5)}

= \frac{- 1 + 25}{\log (5)}

= \frac{24}{\log (5)}

Therefore, the value of the integral is

\frac{24}{\log (5)}

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