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Question 27
Mu
Improper Integrals
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Question
Evaluate
∫
0
∞
e
−
(
x
2
4
+
2025
x
2
)
d
x
\displaystyle\int_0^\infty e^{-\left(\frac{x^2}{4}+\frac{2025}{x^2}\right)}\,dx
∫
0
∞
e
−
(
4
x
2
+
x
2
2025
)
d
x
. You may use
∫
−
∞
∞
e
−
u
2
d
u
=
π
\displaystyle\int_{-\infty}^{\infty}e^{-u^2}\,du=\sqrt\pi
∫
−
∞
∞
e
−
u
2
d
u
=
π
.
A.
e
−
45
π
e^{-45}\sqrt\pi
e
−
45
π
B.
2
e
−
45
π
2e^{-45}\sqrt\pi
2
e
−
45
π
C.
e
−
90
π
e^{-90}\sqrt\pi
e
−
90
π
D.
2
e
−
90
π
2e^{-90}\sqrt\pi
2
e
−
90
π
E.
NOTA
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