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VTRMC
2004 VTRMC
Problem 5
Problem 5
Part of
2004 VTRMC
Problems
(1)
int^x_0 sin(t^2-t+x)dt=f(x), find f''(x)+f(x)
Source: VTRMC 2004 P5
7/27/2021
Let
f
(
x
)
=
∫
0
x
sin
(
t
2
−
t
+
x
)
d
t
f(x)=\int^x_0\sin(t^2-t+x)dt
f
(
x
)
=
∫
0
x
sin
(
t
2
−
t
+
x
)
d
t
. Compute
f
′
′
(
x
)
+
f
(
x
)
f''(x)+f(x)
f
′′
(
x
)
+
f
(
x
)
and deduce that
f
(
12
)
(
0
)
+
f
(
10
)
(
0
)
=
0
f^{(12)}(0)+f^{(10)}(0)=0
f
(
12
)
(
0
)
+
f
(
10
)
(
0
)
=
0
.
integration
calculus