Evaluate the definite integral in Exercise: _ 4 ^ 5 e^ x dx - Vidyadip

Question

Evaluate the definite integral in Exercise:
$\int\limits_{4}^{5}\text{e}^{\text{x}}\ \text{dx}$

✓

Answer

$\text{Let}\ \text{I}=\int\limits_{4}^{5}\text{e}^{\text{x}}\ \text{dx}$

$\int\text{e}^\text{x}\ \text{dx}=\text{e}^\text{x}=\text{F}\text{(x)}$

By second fundamental theorem of calculus, we obtain

$\text{I}=\text{F}(5)-\text{F}(4)$

$=\text{e}^{5}-\text{e}^{4}$

$=\text{e}^{4}(\text{e}-1)$

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