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Explain why each of the following integrals is improper.

(a) $ \displaystyle \int_1^2 \frac{x}{x - 1}\ dx $(b) $ \displaystyle \int_0^\infty \frac{1}{1 + x^3}\ dx $(c) $ \displaystyle \int_{-\infty}^\infty x^2 e^{-x^2}\ dx $(d) $ \displaystyle \int_0^{\frac{\pi}{4}} \cot x\ dx $

a. Type 2 improper integral.b. improper integral of Type 1.c. improper integral of Type 1.d. Type 2 improper integral.

Calculus 2 / BC

Chapter 7

Techniques of Integration

Section 8

Improper Integrals

Integration Techniques

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