Evaluate
\frac{189}{16}=11.8125
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\int 42x\mathrm{d}x
Evaluate the indefinite integral first.
42\int x\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.
21x^{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 42 times \frac{x^{2}}{2}.
21\times \left(\frac{3}{4}\right)^{2}-21\times 0^{2}
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{189}{16}
Simplify.
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