Menu Close

what-the-prove-that-a-b-f-x-dx-a-b-f-a-b-x-dx-

Tinku Tara 0 Comments
Pin




Question Number 70818 by oyemi kemewari last updated on 08/Oct/19
what the prove that ∫_a ^b f(x) dx =∫_a ^b f(a+b−x) dx
whattheprovethat∫abf(x)dx=∫abf(a+b−x)dx
Commented by kaivan.ahmadi last updated on 08/Oct/19
u=a+b−x⇒du=−dx { ((x=a⇒u=b)),((x=b⇒u=a)) :} ⇒∫_a ^b f(a+b−x)dx=∫_b ^a −f(u)du=∫_a ^b f(u)du=∫_a ^b f(x)dx
u=a+b−x⇒du=−dx{x=a⇒u=bx=b⇒u=a⇒∫abf(a+b−x)dx=∫ba−f(u)du=∫abf(u)du=∫abf(x)dx
Answered by MJS last updated on 08/Oct/19
∫_a ^b f(x)dx=[F(x)]_a ^b =F(b)−F(a) ∫_a ^b f(a+b−x)dx= [t=a+b−x ⇒ dx=−dt] =−∫_b ^a f(t)dt=−[F(t)]_b ^a =[F(t)]_a ^b =F(b)−F(a)
∫baf(x)dx=[F(x)]ab=F(b)−F(a)∫baf(a+b−x)dx=[t=a+b−x⇒dx=−dt]=−∫abf(t)dt=−[F(t)]ba=[F(t)]ab=F(b)−F(a)

Pin

Leave a Reply

Your email address will not be published. Required fields are marked *