∫ (from 0 to 1) of (3/2sqrt{x}-2) wrt x eching

$$\int _ { 0 } ^ { 1 } ( \frac { 3 } { 2 } \sqrt { x } - 2 ) d x$$

Baholash

$$-1$$

Yechim qadamlari

Avval noaniq integralni baholang.

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

Summani muddatma-muddat integratsiya qiling.

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

Har bir shartda konstantani qavsdan tashqariga oling.

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

\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. \frac{3}{2} ni \frac{2x^{\frac{3}{2}}}{3} marotabaga ko'paytirish.

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

\int a\mathrm{d}x=ax umumiy integrallar qoidasi jadvalidan foydalanib, -2 integralini toping.

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

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

$$1^{\frac{3}{2}}-2-\left(0^{\frac{3}{2}}-2\times 0\right)$$

Qisqartirish.

$$-1$$