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[Solved] Definite Integral

 
Integral
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June 15, 2021 2:53 pm
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(@armor)
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Find the value of  \int_{0}^{1}e^{3x}dx.

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June 15, 2021 2:53 pm
Topic starter
Staff 
(@armor)
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A primitive for \small e^{3x}  is \small \frac{1}{3}e^{3x}  (because   \small \frac{\partial }{\partial x}(\frac{1}{3}e^{3x})=e^{3x} ),   and so the value of the definite integral is

\small \int_{0}^{1}e^{3x}dx=[\frac{1}{3}e^{3x}]_{0}^{1}=\frac{1}{3}e^3-\frac{1}{3}e^0=\frac{1}{3}(e^3-1).

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