Question

Determine o valor da integral

Answer 1

Resposta:

542/4

Explicação passo-a-passo:

$\int\limits^8_1 {\frac{4u^{3}+u^{2}\sqrt[3]{u}-2 }{u^{2} } \, du$

$\int\limits^8_1 {\frac{4u^{3}}{u^{2}}+ \frac{u^{2}\sqrt[3]{u}}{u^{2} }-\frac{2}{u^{2}} \, du$

$\int\limits^8_1 {4u+ \sqrt[3]{u} -\frac{2}{u^{2}} \, du$

$\int\limits^8_1 {4u} \, du+\int\limits^8_1 {\sqrt[3]{u} } \, du+\int\limits^8_1 {\frac{-2}{u^{2}} } \, du$

$4\int\limits^8_1 {u} \, du+\int\limits^8_1 {u^{\frac{1}{3} } } \, du-2\int\limits^8_1 {\frac{1}{u^{2}} } \, du$

$4\int\limits^8_1 {u} \, du+\int\limits^8_1 {u^{\frac{1}{3} } } \, du-2\int\limits^8_1 {u^{-2} } \, du$

$4[\frac{u^{2}}{2} ]^{8}_{1}+[\frac{3}{4}u^{\frac{4}{3} } ]^{8}_{1}-2[-u^{-1}]^{8}_{1}$

$4[\frac{8^{2}}{2} - \frac{1^{2}}{2} ]+[\frac{3}{4}8^{\frac{4}{3} } -\frac{3}{4}1^{\frac{4}{3} } ]-2[-8^{-1} - (-1^{-1})]$

$4[32 - \frac{1}{2} ]+[12 -\frac{3}{4}]-2[-\frac{1}{8} +1]$

$4[\frac{63}{2} ]+[\frac{45}{4}]-2[\frac{7}{8}]$

$\frac{542}{4}$

Answer 2

Resposta:

295/2

Explicação passo-a-passo:

Integrar cada parcela a partir da tabela de integrais e substituir os limites de integração.