Issolvi ∫ (from -9 to 45) of 5x+8585+68*{(e)^15 wrt x

$$\int_{ -9 }^{ 45 } 5x+8585+68 \times {(e)^{ 15 }} d x$$

Evalwa

$$3672e^{15}+468450\approx 12004300241.717580795$$

Passi tas-Soluzzjonijiet

L-ewwel evalwa l-integru indefinit.

$$\int 5x+8585+68e^{15}\mathrm{d}x$$

Tintegra s-somma terminu b'terminu.

$$\int 5x\mathrm{d}x+\int 8585\mathrm{d}x+\int 68e^{15}\mathrm{d}x$$

Iffattura ‘l barra l-kostanti f’kull wieħed minn dawn it-termini.

$$5\int x\mathrm{d}x+\int 8585\mathrm{d}x+68\int e^{15}\mathrm{d}x$$

Minn \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} għal k\neq -1, issostitwixxi \int x\mathrm{d}x ma' \frac{x^{2}}{2}. Immultiplika 5 b'\frac{x^{2}}{2}.

$$\frac{5x^{2}}{2}+\int 8585\mathrm{d}x+68\int e^{15}\mathrm{d}x$$

Sib l-integru ta' 8585 billi tuża t-tabella tar-regola tal-integrali komuni \int a\mathrm{d}x=ax.

$$\frac{5x^{2}}{2}+8585x+68\int e^{15}\mathrm{d}x$$

Sib l-integru ta' e^{15} billi tuża t-tabella tar-regola tal-integrali komuni \int a\mathrm{d}x=ax.

$$\frac{5x^{2}}{2}+8585x+68e^{15}x$$

L-integru definit huwa l-antiderivattiv tal-espressjoni evalwata fil-limitu superjuri tal-integrazzjoni minus l-antiderivattiv evalwat fil-limitu inferjuri tal-integrazzjoni.

$$\frac{5}{2}\times 45^{2}+8585\times 45+68e^{15}\times 45-\left(\frac{5}{2}\left(-9\right)^{2}+8585\left(-9\right)+68e^{15}\left(-9\right)\right)$$

Issimplifika.

$$468450+3672e^{15}$$