Improper integral

19 practice questionsIntegral CalculusStep-by-step solutions

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Evaluate $\displaystyle\int_0^1 \frac{dx}{x}$ (integrand unbounded as $x\to0^+$ ).

A.Diverges (no finite value)

0

1

-\infty

, but treated as

0

by symmetry

Evaluate $\displaystyle\int_0^\infty e^{-x}\,dx$ .

1

0

e

D.Diverges

Evaluate $\displaystyle\int_0^1 \frac{dx}{\sqrt x}$ (the integrand is unbounded as $x\to0^+$ ).

2

B.Diverges

\dfrac12

1

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