Evaluate
\frac{35}{2}=17.5
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\int -x+5\mathrm{d}x
Evaluate the indefinite integral first.
\int -x\mathrm{d}x+\int 5\mathrm{d}x
Integrate the sum term by term.
-\int x\mathrm{d}x+\int 5\mathrm{d}x
Factor out the constant in each of the terms.
-\frac{x^{2}}{2}+\int 5\mathrm{d}x
Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x\mathrm{d}x with \frac{x^{2}}{2}. Multiply -1 times \frac{x^{2}}{2}.
-\frac{x^{2}}{2}+5x
Find the integral of 5 using the table of common integrals rule \int a\mathrm{d}x=ax.
-\frac{4^{2}}{2}+5\times 4-\left(-\frac{\left(-1\right)^{2}}{2}+5\left(-1\right)\right)
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{35}{2}
Simplify.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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y = 3x + 4
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Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}