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Mathematics
Mathematics
Problem
Which of the following definite integrals is improper because the integrand is unbounded at
x
=
2
x=2
x
=
2
within the interval of integration? a)
∫
−
1
1
x
+
2
d
x
\displaystyle \int_{-1}^{1}\sqrt{x+2}\,dx
∫
−
1
1
x
+
2
d
x
b)
∫
2
5
(
x
−
2
)
2
d
x
\displaystyle \int_{2}^{5}(x-2)^2\,dx
∫
2
5
(
x
−
2
)
2
d
x
c)
∫
1
3
1
(
x
−
2
)
2
d
x
\displaystyle \int_{1}^{3}\frac{1}{(x-2)^2}\,dx
∫
1
3
(
x
−
2
)
2
1
d
x
d)
∫
0
3
1
x
2
+
4
d
x
\displaystyle \int_{0}^{3}\frac{1}{x^2+4}\,dx
∫
0
3
x
2
+
4
1
d
x
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