4. Evaluate the improper integral ∫-∞^0 x^n e^x dx where n ≥ 0 is an integer.

Name: 4. Evaluate the improper integral ∫-∞^0 x^n e^x dx where n ≥ 0 is an integer.
Uploaded: 2021-07-15T17:34:55-08:00
Duration: 6 min 4 s
Channel: Ma. Theresa Alin
Description: 4. Evaluate the improper integral ∫-∞^0 x^n e^x dx where n ≥ 0 is an integer.

Question

4. Evaluate the improper integral \( \int_{-\infty}^{0} x^n e^x dx \) where \( n \ge 0 \) is an integer.

          4. Evaluate the improper integral \( \int_{-\infty}^{0} x^n e^x dx \) where \( n \ge 0 \) is an integer.

4. Evaluate the improper integral ∫-∞^0 x^n e^x dx where n ≥ 0 is an integer.

Added by Daniel C.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Ma. Theresa Alin

07/15/2021

Step 1

Step 1: For the first integral \int_{-\infty}^0 x^{n}e^{x}dx, we can rewrite it as \int_{-\infty}^0 x^{n}e^{x}dx = \int_{-\infty}^0 x^{n}e^{x}dx = \lim_{a \to -\infty} \int_{a}^0 x^{n}e^{x}dx. Show more…

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Evaluate the improper integral int_{-infty}^0 x^{n}e^{x}dx where n >= 0 is an integer. 4. Evaluate the improper integral int_{0}^{infty} nedx where n > 0 is an integer.