Całka oznaczona

[maja001]

Jeśli to mozliwe prosze o sprawdzenie:
1.\(\int_{0}^{1} \sqrt{1+x}dx\)
\(\int_{}^{} \sqrt{1+x}dx= \frac{2}{3}(x+1)^\frac{2}{3} +C\)
\(\int_{0}^{1} \sqrt{1+x}dx= \frac{2}{3} \sqrt{8}- \frac{2}{3}\)

2. \(\int_{0}^{ \frac{ \pi }{2} }sinxdx\)
\(\int_{}^{} sinxdx=-cosx + C\)
\(\int_{0}^{ \frac{ \pi }{2} }sinxdx=1\)

3.\(\int_{1}^{2}lnxdx\)
\(\int_{}^{} lnxdx=x(lnx-1) +C\)
\(\int_{1}^{2}lnxdx=2ln2 -ln1 -1\)

[rayman]

3) ok, pamietaj, ze \(ln(1)=0\)

2) ok

1) jest takze ok