Question

∫e的根号下x次方*dx=,上下限为1到4

Answer 1

∫[1→4] e^(√x) dx

令√x=u,则x=u²,dx=2udu,u：1→2

=∫[1→2] 2ue^u du

=2∫[1→2] u de^u

=2ue^u-2∫[1→2] e^u du

=2ue^u-2e^u |[1→2]

=4e²-2e²-2e+2e

=2e²