Problem with integral on WP 34s
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09-18-2021, 04:45 PM
(This post was last modified: 09-18-2021 05:35 PM by Albert Chan.)
Post: #35
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RE: Problem with integral on WP 34s
CASIO is correct !
Let y = x*x, dy = 2x dx, to remove √(x) ∫(1/(√(x)*(1+x)), x) = ∫(2/(1+y*y), y) = 2*atan(y) I(x = 0 .. 1000) = 2*atan(√1000) ≈ 2*(pi/2 - 1/√1000) ≈ 3.078 I(x = 0 .. 1842) ≈ 2*atan(√1842) ≈ 2*(pi/2 - 1/√1842) ≈ 3.095 To numerically calculate the integral (either x or y version), noted that \(\int_0^a = \int_{1/a}^∞ \quad\), a ≥ 0 For calculators without 'inf' feature, we can transform it back to 0 .. 1 http://fmnt.info/blog/20180818_infinite-integrals.html |
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