Questions: ∫₀² 8/(y⁴+1) dy

∫₀² 8/(y⁴+1) dy
Transcript text: $\int_{0}^{2} \frac{8}{y^{4}+1} d y$
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Solution

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Solution Steps

Step 1: Set Up the Integral

We need to evaluate the integral

\[ \int_{0}^{2} \frac{8}{y^{4}+1} \, dy. \]

Step 2: Numerical Integration

Since the integrand \(\frac{8}{y^{4}+1}\) does not have a simple antiderivative, we use numerical integration techniques to approximate the value of the integral over the interval from \(0\) to \(2\).

Step 3: Result of the Integration

The result of the numerical integration is

\[ \int_{0}^{2} \frac{8}{y^{4}+1} \, dy \approx 8.5610, \]

with an estimated error of \(1.1961 \times 10^{-11}\).

Final Answer

Thus, the value of the integral is

\[ \boxed{8.5610}. \]

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