Question

Tính các tích phân sau:

a) \(\int\limits^3_12xdx;\)                 b) \(\int\limits^{\pi}_0\sin tdt;\)               c) \(\int\limits^{\ln2}_0e^udu.\)

Answer 1

a) \(\int\limits_1^3 {2xdx}  = \left. {{x^2}} \right|_1^3 = {3^2} - {1^2} = 8\)

b) \(\int\limits_0^\pi  {\sin tdt}  = \left. {\left( { - \cos t} \right)} \right|_0^\pi  = \left( { - \cos \pi } \right) - \left( { - \cos 0} \right) = 2\)

c) \(\int\limits_0^{\ln 2} {{e^u}du}  = \left. {{e^u}} \right|_0^2 = {e^2} - {e^0} = {e^2} - 1\)