Datrys ∫ (from 0 to 3) of 30.7+0.81t^2+0.1215t^4+0.01215t^6dt

$$\int _ { 0 } ^ { 3 } 30.7 + 0.81 t ^ { 2 } + 0.1215 t ^ { 4 } + 0.01215 t ^ { 6 } d t$$

Enrhifo

$$\frac{15272727}{140000}\approx 109.090907143$$

Camau Ateb

Gwerthuso’r integryn amhenodol yn gyntaf.

$$\int 30.7+\frac{81t^{2}}{100}+\frac{243t^{4}}{2000}+\frac{243t^{6}}{20000}\mathrm{d}t$$

Integreiddio'r swm fesul term.

$$\int 30.7\mathrm{d}t+\int \frac{81t^{2}}{100}\mathrm{d}t+\int \frac{243t^{4}}{2000}\mathrm{d}t+\int \frac{243t^{6}}{20000}\mathrm{d}t$$

Ffactoreiddio allan y cysonyn ym mhob un o'r termau.

$$\int 30.7\mathrm{d}t+\frac{81\int t^{2}\mathrm{d}t}{100}+\frac{243\int t^{4}\mathrm{d}t}{2000}+\frac{243\int t^{6}\mathrm{d}t}{20000}$$

Canfod integryn 30.7 gan ddefnyddio'r rheol tabl o integrynnau cyffredin \int a\mathrm{d}t=at.

$$\frac{307t}{10}+\frac{81\int t^{2}\mathrm{d}t}{100}+\frac{243\int t^{4}\mathrm{d}t}{2000}+\frac{243\int t^{6}\mathrm{d}t}{20000}$$

Ers \int t^{k}\mathrm{d}t=\frac{t^{k+1}}{k+1} ar gyfer k\neq -1, disodli \int t^{2}\mathrm{d}t gyda \frac{t^{3}}{3}. Lluoswch 0.81 â \frac{t^{3}}{3}.

$$\frac{307t}{10}+\frac{27t^{3}}{100}+\frac{243\int t^{4}\mathrm{d}t}{2000}+\frac{243\int t^{6}\mathrm{d}t}{20000}$$

Ers \int t^{k}\mathrm{d}t=\frac{t^{k+1}}{k+1} ar gyfer k\neq -1, disodli \int t^{4}\mathrm{d}t gyda \frac{t^{5}}{5}. Lluoswch 0.1215 â \frac{t^{5}}{5}.

$$\frac{307t}{10}+\frac{27t^{3}}{100}+\frac{243t^{5}}{10000}+\frac{243\int t^{6}\mathrm{d}t}{20000}$$

Ers \int t^{k}\mathrm{d}t=\frac{t^{k+1}}{k+1} ar gyfer k\neq -1, disodli \int t^{6}\mathrm{d}t gyda \frac{t^{7}}{7}. Lluoswch 0.01215 â \frac{t^{7}}{7}.

$$\frac{307t}{10}+\frac{27t^{3}}{100}+\frac{243t^{5}}{10000}+\frac{243t^{7}}{140000}$$

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.

$$30.7\times 3+\frac{27}{100}\times 3^{3}+\frac{243}{10000}\times 3^{5}+\frac{243}{140000}\times 3^{7}-\left(30.7\times 0+\frac{27}{100}\times 0^{3}+\frac{243}{10000}\times 0^{5}+\frac{243}{140000}\times 0^{7}\right)$$

Symleiddio.

$$\frac{15272727}{140000}$$