question archive Explain why each of the following integrals is improper
Explain why each of the following integrals is improper
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Explain why each of the following integrals is improper. (a) integrate limit 6 to 7 x/x-6 dx Since the integral has an infinite interval of integration, it is a Type 1 improper integral. Since the integral has an infinite discontinuity, it is a Type 2 improper integral. The integral is a proper integral. (b) integrate limit 0 to infinity 1/1+x^3 dx Since the integral has an infinite interval of integration, it is a Type 1 improper integral. Since the integral has an infinite discontinuity, it is a Type 2 improper integral. The integral is a proper integral. (c) integrate limit- infinity to infinity x^2e^-x^2 dx Since the integral has an infinite interval of integration, it is a Type 1 improper integral. Since the integral has an infinite discontinuity, it is a Type 2 improper integral. The integral is a proper integral. (d) integrate limit 0 to pi/4 cot x dx Since the integral has an infinite interval of integration, it is a Type 1 improper integral. Since the integral has an infinite discontinuity, it is a Type 2 improper integral. The integral is a proper integral.
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