Evaluate
\frac{1}{4}=0.25
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\int -1+\frac{x}{2}\mathrm{d}x
Evaluate the indefinite integral first.
\int -1\mathrm{d}x+\int \frac{x}{2}\mathrm{d}x
Integrate the sum term by term.
\int -1\mathrm{d}x+\frac{\int x\mathrm{d}x}{2}
Factor out the constant in each of the terms.
-x+\frac{\int x\mathrm{d}x}{2}
Find the integral of -1 using the table of common integrals rule \int a\mathrm{d}x=ax.
-x+\frac{x^{2}}{4}
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 \frac{1}{2} times \frac{x^{2}}{2}.
-3+\frac{3^{2}}{4}-\left(-2+\frac{2^{2}}{4}\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{1}{4}
Simplify.
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\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
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Limits
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