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?Explain why each of the following integrals is improper.(a) \(\int_{1}^{4} \frac{d
Chapter 7, Problem 1(choose chapter or problem)
Explain why each of the following integrals is improper.
(a) \(\int_{1}^{4} \frac{d x}{x\ -\ 3}\)
(b) \(\int_{3}^{\infty} \frac{d x}{x^{2}\ -\ 4}\)
(c) \(\int_{0}^{1} \tan \pi x \ d x\)
(d) \(\int_{-\infty}^{-1} \frac{e^{x}}{x} \ d x\)
Equation Transcription:
∫
∫
∫ tan
x dx
∫
dx
Text Transcription:
integral _1 ^4 dx/x-3
integral _3 ^infinity dx/x^2-4
integral _0 ^1 tan pi x dx
integral _-infinity ^-1 e^x/x dx
Questions & Answers
QUESTION:
Explain why each of the following integrals is improper.
(a) \(\int_{1}^{4} \frac{d x}{x\ -\ 3}\)
(b) \(\int_{3}^{\infty} \frac{d x}{x^{2}\ -\ 4}\)
(c) \(\int_{0}^{1} \tan \pi x \ d x\)
(d) \(\int_{-\infty}^{-1} \frac{e^{x}}{x} \ d x\)
Equation Transcription:
∫
∫
∫ tan
x dx
∫
dx
Text Transcription:
integral _1 ^4 dx/x-3
integral _3 ^infinity dx/x^2-4
integral _0 ^1 tan pi x dx
integral _-infinity ^-1 e^x/x dx
ANSWER:Step 1 of 5
Improper integrals of Type 1
At least one of the upper/lower limit of the definite integral is
Improper integrals of Type 2
The integrand is NOT continuous at ALL points between and including the limits of integration.