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Definite Integrals
The definite integral of a function computes the area under the graph of its curve, allowing us to calculate areas and volumes that are not easily done using geometry alone.
What is the value of the definite integral \[\int_{0}^{1}(9+3x^2)dx?\]
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Evaluate \[ \int_{-2}^{-1}\left( x^3+3x^2+7 \right)dx + \int_{-1}^{2}\left( y^3+3y^2+7 \right)dy. \]
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If \[\int_{0}^{10}f(x)dx=25 \text{ and } \int_{0}^{8}2f(x)dx=22,\] what is the value of \[\int_{8}^{10}f(x)dx?\]
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Consider the limit \[\lim_{n \to \infty} \sum_{i=1}^{n} \left(x_i^{10}+x_i \sin x_i\right) \Delta x.\] Which of the following definite integrals expresses this limit on the interval \([0, \pi]?\)
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