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Mathematics
Mathematics
Problem
For the function
p
(
x
)
=
4
x
−
1
p(x)=4x-1
p
(
x
)
=
4
x
−
1
, the average value on the interval
[
0
,
b
]
[0,b]
[
0
,
b
]
equals
7
7
7
, where
b
>
0
b>0
b
>
0
. a. (i) Evaluate
∫
0
b
p
(
x
)
d
x
\displaystyle \int_0^b p(x)\,dx
∫
0
b
p
(
x
)
d
x
. b. (ii) Form an equation in
b
b
b
corresponding to the given average value and hence determine the value of
b
b
b
.
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