Evaluate
\frac{675}{2}=337.5
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\int 45-3x\mathrm{d}x
Evaluate the indefinite integral first.
\int 45\mathrm{d}x+\int -3x\mathrm{d}x
Integrate the sum term by term.
\int 45\mathrm{d}x-3\int x\mathrm{d}x
Factor out the constant in each of the terms.
45x-3\int x\mathrm{d}x
Find the integral of 45 using the table of common integrals rule \int a\mathrm{d}x=ax.
45x-\frac{3x^{2}}{2}
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 -3 times \frac{x^{2}}{2}.
45\times 15-\frac{3}{2}\times 15^{2}-\left(45\times 0-\frac{3}{2}\times 0^{2}\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{675}{2}
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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