∫ (from 0 to 04) of -3x-(sqrt{x}) wrt x eching

$$\int _ { 0 } ^ { 04 } - 3 x - ( \sqrt { x } ) d x$$

Baholash

$$0$$

Yechim qadamlari

Avval noaniq integralni baholang.

$$\int -3x-\sqrt{x}\mathrm{d}x$$

Summani muddatma-muddat integratsiya qiling.

$$\int -3x\mathrm{d}x+\int -\sqrt{x}\mathrm{d}x$$

Har bir shartda konstantani qavsdan tashqariga oling.

$$-3\int x\mathrm{d}x-\int \sqrt{x}\mathrm{d}x$$

k\neq -1 uchun integral \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} boʻlgani uchun, \int x\mathrm{d}x integralni \frac{x^{2}}{2} bilan almashtiring. -3 ni \frac{x^{2}}{2} marotabaga ko'paytirish.

$$-\frac{3x^{2}}{2}-\int \sqrt{x}\mathrm{d}x$$

\sqrt{x} ni x^{\frac{1}{2}} sifatida qaytadan yozish. k\neq -1 uchun integral \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} boʻlgani uchun, \int x^{\frac{1}{2}}\mathrm{d}x integralni \frac{x^{\frac{3}{2}}}{\frac{3}{2}} bilan almashtiring. Qisqartirish. -1 ni \frac{2x^{\frac{3}{2}}}{3} marotabaga ko'paytirish.

$$-\frac{3x^{2}}{2}-\frac{2x^{\frac{3}{2}}}{3}$$

Xos integral bu integral hisoblashning yuqori chegarasida hisoblangan ifodaning boshlangʻich holatidan chiqarib tashlagan holda integral hisoblashning quyi chegarasida hisoblangan ifodaning boshlangʻich holatidir.

$$-\frac{3}{2}\times \left(0\times 4\right)^{2}-\frac{2}{3}\times \left(0\times 4\right)^{\frac{3}{2}}-\left(-\frac{3}{2}\times 0^{2}-\frac{2}{3}\times 0^{\frac{3}{2}}\right)$$

Qisqartirish.

$$\text{Indeterminate}$$