Evaluate
\frac{e}{5}\approx 0.543656366
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\int _{0}^{1}x^{4}e\mathrm{d}x
To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.
\int x^{4}e\mathrm{d}x
Evaluate the indefinite integral first.
e\int x^{4}\mathrm{d}x
Factor out the constant using \int af\left(x\right)\mathrm{d}x=a\int f\left(x\right)\mathrm{d}x.
e\times \frac{x^{5}}{5}
Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x^{4}\mathrm{d}x with \frac{x^{5}}{5}.
\frac{ex^{5}}{5}
Simplify.
\frac{1}{5}e\times 1^{5}-\frac{1}{5}e\times 0^{5}
The definite integral is the antiderivative of the expression evaluated at the upper limit of integration minus the antiderivative evaluated at the lower limit of integration.
\frac{e}{5}
Simplify.
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Limits
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