Baholash
1902
Baham ko'rish
Klipbordga nusxa olish
\int 3x^{5}-2x^{3}+x\mathrm{d}x
Evaluate the indefinite integral first.
\int 3x^{5}\mathrm{d}x+\int -2x^{3}\mathrm{d}x+\int x\mathrm{d}x
Integrate the sum term by term.
3\int x^{5}\mathrm{d}x-2\int x^{3}\mathrm{d}x+\int x\mathrm{d}x
Factor out the constant in each of the terms.
\frac{x^{6}}{2}-2\int x^{3}\mathrm{d}x+\int x\mathrm{d}x
Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x^{5}\mathrm{d}x with \frac{x^{6}}{6}. 3 ni \frac{x^{6}}{6} marotabaga ko'paytirish.
\frac{x^{6}}{2}-\frac{x^{4}}{2}+\int x\mathrm{d}x
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}. -2 ni \frac{x^{4}}{4} marotabaga ko'paytirish.
\frac{x^{6}-x^{4}+x^{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}.
\frac{4^{6}}{2}-\frac{4^{4}}{2}+\frac{4^{2}}{2}-\left(\frac{2^{6}}{2}-\frac{2^{4}}{2}+\frac{2^{2}}{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.
1902
Qisqartirish.
Misollar
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