Can anyone explain the answer to #63 on 8767?
Let $$f$$ be a continuous, strictly decreasing, realvalued function such that $$\int_0^\infty f(x)dx$$ is finite and $$f(0)=1$$. In terms of $$f^{1}$$ (the inverse function of $$f$$), $$\int_0^\infty f(x)dx$$ is...
(a) less than $$\int_1^{\infty} f^{1}(y)dy$$
(b) greater than $$\int_0^{1} f^{1}(y)dy$$
(c) equal to $$\int_1^{\infty} f^{1}(y)dy$$
(d) equal to $$\int_0^{1} f^{1}(y)dy$$
(e) equal to $$\int_0^{\infty} f^{1}(y)dy$$
The answer is D.
8767 #63

 Posts: 1
 Joined: Thu Oct 23, 2014 4:12 am
Re: 8767 #63
just sketch the graph of the function
shade the region of the given integral
rotate your paper and you will see why the answer is D
shade the region of the given integral
rotate your paper and you will see why the answer is D