Proove that: #int _a^b f (x)dx= int_a^b f (a+b-x)dx# ?

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Answer 1 · 2018-04-12T07:15:03

Let #u=a+b−x#

#=> du=−dx#

#int_a^b f(x) dx = int_a^b f(u) du# #color(white)(ww#

# "changing limits, " ["when " u = a ; x=b]#
#color(white)(chenging lmwits# #[ "when " u = b ; x=a]#

# => int_b^a f(a+b-x) (-dx)#

# =>- int_b^a f(a+b-x) dx#

# => int_a^b f(a+b-x) dx#

Hence Proved.