Datrys ∫ (from 1 to 4) of x^2+1/x^3 wrt x

$$\int_{ 1 }^{ 4 } { x }^{ 2 } + \frac{ 1 }{ { x }^{ 3 } } d x$$

Enrhifo

$$\frac{687}{32}=21.46875$$

Camau Ateb

Gwerthuso’r integryn amhenodol yn gyntaf.

$$\int x^{2}+\frac{1}{x^{3}}\mathrm{d}x$$

Integreiddio'r swm fesul term.

$$\int x^{2}\mathrm{d}x+\int \frac{1}{x^{3}}\mathrm{d}x$$

Ers \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} ar gyfer k\neq -1, disodli \int x^{2}\mathrm{d}x gyda \frac{x^{3}}{3}.

$$\frac{x^{3}}{3}+\int \frac{1}{x^{3}}\mathrm{d}x$$

Ers \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} ar gyfer k\neq -1, disodli \int \frac{1}{x^{3}}\mathrm{d}x gyda -\frac{1}{2x^{2}}.

$$\frac{x^{3}}{3}-\frac{1}{2x^{2}}$$

Yr integryn pendant yw integryn amhendant y mynegiant wedi’i werthuso ar lefel uchaf yr integreiddiad llai’r integryn amhendant ar lefel isaf yr integreiddiad.

$$\frac{4^{3}}{3}-\frac{4^{-2}}{2}-\left(\frac{1^{3}}{3}-\frac{1^{-2}}{2}\right)$$

Symleiddio.

$$\frac{687}{32}$$