5.3 The Fundamental Theorem of Calculus/9: Difference between revisions
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| <math>g(y)= \int_{y}^{2}t^2\sin{(t)}dt | | <math>g(y)= \int_{y}^{2}t^2\sin{(t)}dt = 9 </math> |
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| = </math> | |
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| int_{0}^{1}\left(3+x\sqrt{x}\right)dx &= \int_{0}^{1}\left(3+x^{1}{x}^{\frac{1}{2}}\right)dx = \int_{0}^{1}\left(3+x^{1+\frac{1}{2}}\right)dx = \int_{0}^{1}\left(3+x^{\frac{3}{2}}\right)dx \\[2ex]
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| &= 3x+\frac{x^{\frac{3}{2}+1}}{\frac{3}{2}+1}\bigg|_{0}^{1} = 3x+\frac{x^{\tfrac{5}{2}}}{\frac{5}{2}}\bigg|_{0}^{1} = 3x+\frac{2x^{\frac{5}{2}}}{5}\bigg|_{0}^{1} \\[2ex]
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Revision as of 16:06, 25 August 2022
