PLEASE EXPLAIN WHY ITS TRUE OR FALSE I need to understand th

PLEASE EXPLAIN WHY ITS TRUE OR FALSE, I need to understand the concepts. Will rate best answer, thank you!

State if the following statements are true or false by marking the appropriate box. (a) If f(x) 13 then f f(x)dx 26. True False (a) If f(x) -4 then the integral J-2.5 f(x)d? 6? True False (c) I J()dz 0 and f is differentiable then f(x)0 erent!able then x) = True False (d) The function f(x)-1/z02 has no anti-derivative on (0,1] True False (e) If g(x)

Solution

a)
f(x) > =13 always
So minimum value of f(x) =13
We are integrating it in width of 2
So minimum area = 13*2=26
Integration value will be >=26
Answer: true

b)
False

Here f(x) >=-4
so its value can be anything between -4 to infinity
it might happen that f(x) = 0
In this case value of integration might become 0 as well or less than 6

c)

False
integration = 0 means that area under the curve is 0
function can be 0
But function can also be such that positive area = negative area and thus making total area = 0

d)
anti derivative means integration
f(x) is continuous and its converges in (0,1]
So, f(x) can be integrated in this range
Answer: false

I am allowed to answer only 4 subparts at a time