If f(4)=10 and f' is continuous and the integral of f'(x)dx=18 from 4 to 5, what is the value of f(5)?
回答 (2)
2015-12-08 3:32 am
∫ [4 to 5] f'(x) dx = 18
f(5) - f(4) = 18
f(5) = 18 + f(4)
28
f(5) - f(4) = 18
f(5) = 18 + f(4)
28
2015-12-08 4:18 am
hint:
The first fundamental theorem of calculus says that
if f is continuous on the closed interval [a,b], and F is the indefinite integral of f on [a,b], then
the definite integral f(x)dx from a to b equals F(b)-F(a).
Here you are given f' is the derivative of f, i.e. f is the indefinite integral of f'.
The first fundamental theorem of calculus says that
if f is continuous on the closed interval [a,b], and F is the indefinite integral of f on [a,b], then
the definite integral f(x)dx from a to b equals F(b)-F(a).
Here you are given f' is the derivative of f, i.e. f is the indefinite integral of f'.
參考: See the theorem at
http://mathworld.wolfram.com/FundamentalTheoremsofCalculus.html
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