∫ (from 1 to 4) of 5sqrt[4]{x wrt x eching

$$\int _ { 1 } ^ { 4 } 5 \sqrt[ 4 ] { x } d x$$

Baholash

$$16\sqrt{2}-4\approx 18,627416998$$

Yechim qadamlari

Avval noaniq integralni baholang.

$$\int 5\sqrt[4]{x}\mathrm{d}x$$

\int af\left(x\right)\mathrm{d}x=a\int f\left(x\right)\mathrm{d}x yordamidan konstantani qavsdan tashqariga chiqaring.

$$5\int \sqrt[4]{x}\mathrm{d}x$$

\sqrt[4]{x} ni x^{\frac{1}{4}} 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}{4}}\mathrm{d}x integralni \frac{x^{\frac{5}{4}}}{\frac{5}{4}} bilan almashtiring. Qisqartirish. 5 ni \frac{4x^{\frac{5}{4}}}{5} marotabaga ko'paytirish.

$$4x^{\frac{5}{4}}$$

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

$$4\times 4^{\frac{5}{4}}-4\times 1^{\frac{5}{4}}$$

Qisqartirish.

$$16\sqrt{2}-4$$