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Choose the correct option.
∫₀¹ (x⁴ - 1)/(x² + 1) dx is equal to:
$\int_0^1 \frac{x^4 - 1}{x^2 + 1}\,dx$ is equal to:
- (a)$\frac{2}{3}$
- (b)$\frac{1}{3}$
- (c)$-\frac{2}{3}$
- (d)$0$
Answer
Answer
Correct option: (c)
Answer: (c) $-\frac{2}{3}$
$\frac{x^4-1}{x^2+1}=x^2-1$, so $\int_0^1 (x^2-1)\,dx=\frac13-1=-\frac23$.