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

  • Page ID
    88685
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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

    This page titled 7.2: Homework- Power, exponential, trig, and logarithmic rules is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Tyler Seacrest via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.