| physics-application |
| rote-problem |
| ucf16-003 Using high-school geometry, compute the following: \begin{align*} \text{a) }&\int_{0}^{2} x dx & \text{b) }&\int_{1}^{4}(1+3x) dx \\ \text{c) }&\int_{-1}^{3}(1-x) dx & \text{d) }&\int_{0}^{1}(1-x^{2})^{1/2} dx \\ \text{e) }&\int_{0}^{1/2} (1-x^{2})^{1/2} dx & \\ \end{align*} |
| ucf16-006
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| ucf16-007 Let \( f(x)= \begin{cases} 0 & \text{when \( x \) is rational} \\ 1 & \text{when \( x \) is irrational} \end{cases}\) and consider a subdivision \( \Delta \) of \( [0,1] \) of one hundred equal subintervals: \( 0 < .01 < .02 < .03 < . . . < .99 < 1 \)
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