Question

求由曲线y=e^x,y=e^2x与y=2所围成平面图形的面积

Answer 1

y=e^x,x=lny

y=e^2x,x=(lny)/2

所以S=∫(1,2)[lny-(lny)/2]dy

=1/2∫(1,2)lnydy

=1/2*ylny-1/2∫(1,2)ydlny

=1/2*ylny-1/2∫(1,2)y*1/ydy

=1/2(ylny-y) (1,2)

=ln2-1/2