Baholash
17
Baham ko'rish
Klipbordga nusxa olish
\int 15x^{2}-12x\mathrm{d}x
Evaluate the indefinite integral first.
\int 15x^{2}\mathrm{d}x+\int -12x\mathrm{d}x
Integrate the sum term by term.
15\int x^{2}\mathrm{d}x-12\int x\mathrm{d}x
Factor out the constant in each of the terms.
5x^{3}-12\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^{2}\mathrm{d}x with \frac{x^{3}}{3}. 15 ni \frac{x^{3}}{3} marotabaga ko'paytirish.
5x^{3}-6x^{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}. -12 ni \frac{x^{2}}{2} marotabaga ko'paytirish.
5\times 2^{3}-6\times 2^{2}-\left(5\times 1^{3}-6\times 1^{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.
17
Qisqartirish.
Misollar
Ikkilik tenglama
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometriya
4 \sin \theta \cos \theta = 2 \sin \theta
Chiziqli tenglama
y = 3x + 4
Arifmetik
699 * 533
Matritsa
\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]
Simli tenglama
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differensatsiya
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Oʻngga
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Chegaralar
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}