# 7.2: Homework- Power, exponential, trig, and logarithmic rules

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1. Compute the following definite integrals.
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. Approximate $$\int_0^1 x^2dx$$ using $$4$$ rectangles. Then find $$\int_0^1 x^2$$ exactly using an anti-derivative. How far off is the approximation?
Approximation $$\approx 0.22$$, the actual is $$\frac{1}{3} \approx .33$$, so the difference is about $$0.11$$ or $$50$$ error which isn't great. As we know, the rectangles don't always do such a good job.
ans

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