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# 7.2: Tear-Poder, exponencial, trigonometría y reglas logarítmicas

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1. Compute las siguientes integrales definidas.
1. $$\int_{2}^3 x^3 + 2 \sqrt{x} dx$$
19.04
ans
2. $$\int_{-2}^3 (x + 5)^2dx$$
$$\approx 161.7$$
ans
3. $$\int_{0}^{1} e^xdx$$
$$e - 1 \approx 1.718$$
ans
4. $$\int_{-1}^1 3 e^xdx$$
$$7.05$$
ans
5. $$\int_{1}^{e} \frac{3}{x} + \frac{x}{3}\ dx$$
$$\approx 4.06$$
ans
2. Aproximado$$\int_0^1 x^2dx$$ usando$$4$$ rectángulos. Entonces encuentra$$\int_0^1 x^2$$ exactamente usando un anti-derivado. ¿Qué tan lejos está la aproximación?
Aproximación$$\approx 0.22$$, lo real es$$\frac{1}{3} \approx .33$$, entonces la diferencia es sobre$$0.11$$ o$$50$$ error que no es grande. Como sabemos, los rectángulos no siempre hacen tan buen trabajo.
ans

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