Chapter 8: Q. 69 (page 702)

Use the results from Exercises 51–60 and Theorem 7.38 to approximate the values of the definite integrals in Exercises 61–70 to within 0.001 of their values.
$\int_{0.5}^{1} x^{2} e^{- 3 x^{2}} dx$

Short Answer

Expert verified

$\int_{0.5}^{1} x^{2} e^{- 3 x^{2}} dx \approx - 0.481$

Step by step solution

Step 1. Given information is:

$\int_{0.5}^{1} x^{2} e^{- 3 x^{2}} dx$

Step 2. Approximating the values

$From Q 59 . \int_{0.5}^{1} x^{2} e^{- 3 x^{2}} dx = \sum_{k = 0}^{\infty} \frac{{(- 1)}^{k} 3^{k}}{k!} (\frac{1 - {(0.5)}^{2 k + 3}}{2 k + 3}) This implies that to approximate the values of integrals, put the value of k \int_{0.5}^{1} x^{2} e^{- 3 x^{2}} dx = \frac{1}{3} (1 - 0 . 5^{4}) - \frac{3}{5} (1 - 0 . 5^{6}) + \frac{9}{2! \cdot 7} (1 - 0 . 5^{8}) = 0.3125 - 0.5906 + 0.6403 - 0.4995 \approx - 0.481$

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Use the results from Exercises 51–60 and Theorem 7.38 to approximate the values of the definite integrals in Exercises 61–70 to within 0.001 of their values.
$\int_{0.5}^{1} x^{2} e^{- 3 x^{2}} dx$

Short Answer

Step by step solution

Step 1. Given information is:

Step 2. Approximating the values

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Use the results from Exercises 51–60 and Theorem 7.38 to approximate the values of the definite integrals in Exercises 61–70 to within 0.001 of their values.∫0.51x2e-3x2dx

Short Answer

Step by step solution

Step 1. Given information is:

Step 2. Approximating the values

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

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Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Use the results from Exercises 51–60 and Theorem 7.38 to approximate the values of the definite integrals in Exercises 61–70 to within 0.001 of their values.
$\int_{0.5}^{1} x^{2} e^{- 3 x^{2}} dx$