Evaluate the following integrals. int_{-1}^1 10^xdx

Question
Integrals
asked 2021-02-06
Evaluate the following integrals.
\(\int_{-1}^1 10^xdx\)

Answers (1)

2021-02-07
\(\text{It is given that}\)
\(\int_{-1}^1 10^xdx\)
\(\text{The given integration can be written as}\)
\(I=\int_{-1}^1 e^{x\ln10}dx\)
\(t=x\ln10\)
\(dx=\frac{1}{\ln10}dt\)
\(\text{The integration wiil be}\)
\(I=\frac{1}{\ln10}\int_{-1}^1 e^tdt\)
\(I=\frac{1}{\ln10}[e^t]_{-1}^1\)
\(\text{Put }t=x\ln10\)
\(I=\frac{1}{\ln10}[10^x]_{-1}^1\)
\(I=\frac{1}{\ln10}[10^1-10^{-1}]\)
\(=\frac{99}{10\ln10}\)
\(\text{Hence the value of integration is }\frac{99}{10\ln10}\)
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