1 of 6
Mathematics AA
HL only
Paper 3 · calculator
AHL5.16
AHL1.15
Question 1 · 24 marks
Spec and skills
Spec AHL5.16
Spec AHL1.15
For integers
n
≥
0
n\ge0
n
≥
0
,
let
I
n
=
∫
0
1
x
n
e
x
d
x
I_n=\displaystyle\int_0^1x^ne^x\,dx
I
n
=
∫
0
1
x
n
e
x
d
x
.
The graph shows
y
=
e
x
y=e^x
y
=
e
x
on
0
≤
x
≤
1
0\le x\le1
0
≤
x
≤
1
.
0
0.25
0.5
0.75
1
1
2
3
x
x
x
y
y
y
y
y
y
=
e
x
=e^x
=
e
x
(a)
Find the exact values of
I
0
I_{0}
I
0
and
I
1
I_{1}
I
1
.
3 marks
I
0
=
I_0 =
I
0
=
I
1
=
I_1 =
I
1
=
xⁿ
a/b
√
π
(
)