By using a suitable substitution, show that
in(with upper limit = b & lower limit = a) f(x) dx = in(with upper limit = b & lower limit = a) f(a+b-x) dx
where f(x) is a continuous function defined on [a,b]
Thanks
Maths Integration
2012-03-24 8:54 am
回答 (1)
2012-03-24 11:53 pm
✔ 最佳答案
Use the substitute x = a + b - y.When x = a, y = b
When x = b, y = a
dx = d(a + b - y) = - dy.
So ∫ f(x) dx from a to b
= ∫ f(a + b - y)(- dy) from b to a
= ∫ f(a + b - y)dy from a to b
= ∫ f(a + b - x)dx from a to b.
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