Answer
a) Improper. The function $x^{-\frac{1}{3}}$ is infinite at 0
b) Improper. Infinite interval of intergration
c) Improper. Infinite interval of intergration
d) Proper, The function $e^{-x}$ is continuous on the finite interval [0,1]
e) Improper. The function sec x is infinite at $\frac{\pi}{2}$
f) Improper. Infinite interval of intergration
g) Proper, The function sin x is continuous on the finite interval [0,1]
h) Proper, The function $\frac{1}{\sqrt {3-x^{2}}}$ is continuous on the finite interval [0,1]
i) Improper. Infinite interval of intergration
j) Improper. The function $\ln{x}$ is infinite at 0
Work Step by Step
a) Improper. The function $x^{-\frac{1}{3}}$ is infinite at 0
b) Improper. Infinite interval of intergration
c) Improper. Infinite interval of intergration
d) Proper, The function $e^{-x}$ is continuous on the finite interval [0,1]
e) Improper. The function sec x is infinite at $\frac{\pi}{2}$
f) Improper. Infinite interval of intergration
g) Proper, The function sin x is continuous on the finite interval [0,1]
h) Proper, The function $\frac{1}{\sqrt {3-x^{2}}}$ is continuous on the finite interval [0,1]
i) Improper. Infinite interval of intergration
j) Improper. The function $\ln{x}$ is infinite at 0
