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\int _{0}^{4}x^{2}x\mathrm{d}x
Multiply -1 and -1 to get 1.
\int _{0}^{4}x^{3}\mathrm{d}x
To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.
\int x^{3}\mathrm{d}x
Evaluate the indefinite integral first.
\frac{x^{4}}{4}
Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x^{3}\mathrm{d}x with \frac{x^{4}}{4}.
\frac{4^{4}}{4}-\frac{0^{4}}{4}
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.
64
Simplify.
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{ x } ^ { 2 } - 4 x - 5 = 0
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y = 3x + 4
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Matrix
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Simultaneous equation
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\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
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