Question

大一数学。圈起来的两题。急，谢谢

大一数学。圈起来的两题。急，谢谢要过程。谢谢了

Answer 1

Answer 2

(1)
let
x=a+b-y
dx = -dy
x=a, y=b
x=b, y=a
∫(a->b) f(x) dx
=∫(b->a) f(a+b-y) (-dy)
=∫(a->b) f(a+b-y) dy
(3)
let
x=2a-y
dx =-dy
x=a, y=a
x=2a, y=0
∫(0->2a) f(x) dx
=∫(0->a) f(x) dx +∫(a->2a) f(x) dx
=∫(0->a) f(x) dx +∫(a->0) f(2a-y) (-dy)
=∫(0->a) f(x) dx +∫(0->a) f(2a-y) dy
=∫(0->a) f(x) dx +∫(0->a) f(2a-x) dx
=∫(0->a) [f(x) +f(2a-x)] dx