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Simon Marais Mathematical Competition
2019 Simon Marais Mathematical Competition
B1
Maximizing the integral
Maximizing the integral
Source: Simon Marais MC 2019 B1
October 14, 2019
calculus
integration
Problem Statement
Determine all pairs
(
a
,
b
)
(a,b)
(
a
,
b
)
of real numbers with
a
⩽
b
a\leqslant b
a
⩽
b
that maximise the integral
∫
a
b
e
cos
(
x
)
(
380
−
x
−
x
2
)
d
x
.
\int_a^b e^{\cos (x)}(380-x-x^2) \mathrm{d} x.
∫
a
b
e
c
o
s
(
x
)
(
380
−
x
−
x
2
)
d
x
.
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