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@@ -37,7 +37,7 b'' | |||||
37 | "cell_type": "code", |
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37 | "cell_type": "code", | |
38 | "execution_count": 2, |
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38 | "execution_count": 2, | |
39 | "metadata": { |
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39 | "metadata": { | |
40 |
"collapsed": |
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40 | "collapsed": false | |
41 | }, |
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41 | }, | |
42 | "outputs": [], |
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42 | "outputs": [], | |
43 | "source": [ |
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43 | "source": [ | |
@@ -63,9 +63,10 b'' | |||||
63 | }, |
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63 | }, | |
64 | "outputs": [], |
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64 | "outputs": [], | |
65 | "source": [ |
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65 | "source": [ | |
66 | "a, b = 1, 9\n", |
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66 | "a, b = 1, 8 # the left and right boundaries\n", | |
67 | "xint = x[np.logical_and(x>=a, x<=b)][::30]\n", |
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67 | "N = 5 # the number of points\n", | |
68 | "yint = y[np.logical_and(x>=a, x<=b)][::30]" |
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68 | "xint = np.linspace(a, b, N)\n", | |
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69 | "yint = f(xint)" | |||
69 | ] |
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70 | ] | |
70 | }, |
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71 | }, | |
71 | { |
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72 | { | |
@@ -85,250 +86,255 b'' | |||||
85 | { |
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86 | { | |
86 | "data": { |
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87 | "data": { | |
87 | "image/png": [ |
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88 | "image/png": [ | |
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327 | "wWqlqxBEJBJ4EnjIGPOU0/F0Zn9dfw1rETYnXQAsFZFdwKNAuYj81uGYMMYcsl+PAH/A6m500n5g\n", | |
327 | "EaFcvXq1yc+Qi5iEEKID6tzDE4QQooOScBdCiA5Iwl0IITogCXchhOiAJNyFEKIDknAXQogOSMJd\n", |
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328 | "f6dvVKuwEny4WAK8b/99OW0RsMsYU22MaQN+j/XvzFHGmPuMMdONMfOBWqznamcYzIT+F6BQRPLs\n", | |
328 | "CCE6IAl3IYTogP4/oENi/a9Z/A8AAAAASUVORK5CYII=\n" |
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329 | "38jXAc8M4v2HDBER4DfARmPMT52OB0BEUkQkwX7vBS7E6tt3jDHmX4wxOcaYMVhf2f9kjLnFyZhE\n", | |
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330 | "xCcisfZ7P3AR1gMtxxhjDgP7RKRjVcNFwCcOhnS6ZVi/kMPBHmCWiHjt/w8XARsdjgkRSbNfR2Nt\n", | |||
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331 | "+BOye6q/13LpkgnDSUci8igwH0gWkX3At40xK52MyTYba2OPj0TkQ/vYncaYFx2MKRN4wF4i2QU8\n", | |||
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332 | "box53sF4QgmHbr104A9WLiACeNgY87KzIQHwt8DDdmNqB7DC4XiAT3/pLeLUNpOOMsa8KyKrsNaP\n", | |||
|
333 | "arNff+1sVACsEpFkoBW43RhzIlQlnViklFLDxFDYgk4ppVQPaEJXSqlhQhO6UkoNE5rQlVJqmNCE\n", | |||
|
334 | "rpRSw4QmdKWUGiY0oSul1DChCV0ppYaJ/w8u1j+cuZEJ1QAAAABJRU5ErkJggg==\n" | |||
329 | ], |
|
335 | ], | |
330 | "text/plain": [ |
|
336 | "text/plain": [ | |
331 |
"<matplotlib.figure.Figure at 0x |
|
337 | "<matplotlib.figure.Figure at 0x7f47175e3898>" | |
332 | ] |
|
338 | ] | |
333 | }, |
|
339 | }, | |
334 | "metadata": {}, |
|
340 | "metadata": {}, | |
@@ -337,7 +343,7 b'' | |||||
337 | ], |
|
343 | ], | |
338 | "source": [ |
|
344 | "source": [ | |
339 | "plt.plot(x, y, lw=2)\n", |
|
345 | "plt.plot(x, y, lw=2)\n", | |
340 |
"plt.axis([0, |
|
346 | "plt.axis([0, 9, 0, 140])\n", | |
341 | "plt.fill_between(xint, 0, yint, facecolor='gray', alpha=0.4)\n", |
|
347 | "plt.fill_between(xint, 0, yint, facecolor='gray', alpha=0.4)\n", | |
342 | "plt.text(0.5 * (a + b), 30,r\"$\\int_a^b f(x)dx$\", horizontalalignment='center', fontsize=20);" |
|
348 | "plt.text(0.5 * (a + b), 30,r\"$\\int_a^b f(x)dx$\", horizontalalignment='center', fontsize=20);" | |
343 | ] |
|
349 | ] | |
@@ -360,21 +366,39 b'' | |||||
360 | "name": "stdout", |
|
366 | "name": "stdout", | |
361 | "output_type": "stream", |
|
367 | "output_type": "stream", | |
362 | "text": [ |
|
368 | "text": [ | |
363 |
"The integral is: |
|
369 | "The integral is: 565.2499999999999 +/- 6.275535646693696e-12\n", | |
364 |
"The trapezoid approximation with |
|
370 | "The trapezoid approximation with 5 points is: 559.890625\n" | |
365 | ] |
|
371 | ] | |
366 | } |
|
372 | } | |
367 | ], |
|
373 | ], | |
368 | "source": [ |
|
374 | "source": [ | |
369 | "from __future__ import print_function\n", |
|
375 | "from __future__ import print_function\n", | |
370 |
"from scipy.integrate import quad |
|
376 | "from scipy.integrate import quad\n", | |
371 |
"integral, error = quad(f, |
|
377 | "integral, error = quad(f, a, b)\n", | |
|
378 | "integral_trapezoid = sum( (xint[1:] - xint[:-1]) * (yint[1:] + yint[:-1]) ) / 2\n", | |||
372 | "print(\"The integral is:\", integral, \"+/-\", error)\n", |
|
379 | "print(\"The integral is:\", integral, \"+/-\", error)\n", | |
373 |
"print(\"The trapezoid approximation with\", len(xint), \"points is:\", |
|
380 | "print(\"The trapezoid approximation with\", len(xint), \"points is:\", integral_trapezoid)" | |
374 | ] |
|
381 | ] | |
375 | } |
|
382 | } | |
376 | ], |
|
383 | ], | |
377 |
"metadata": { |
|
384 | "metadata": { | |
|
385 | "kernelspec": { | |||
|
386 | "display_name": "Python 3", | |||
|
387 | "name": "python3" | |||
|
388 | }, | |||
|
389 | "language_info": { | |||
|
390 | "codemirror_mode": { | |||
|
391 | "name": "ipython", | |||
|
392 | "version": 3 | |||
|
393 | }, | |||
|
394 | "file_extension": ".py", | |||
|
395 | "mimetype": "text/x-python", | |||
|
396 | "name": "python", | |||
|
397 | "nbconvert_exporter": "python", | |||
|
398 | "pygments_lexer": "ipython3", | |||
|
399 | "version": "3.4.2" | |||
|
400 | } | |||
|
401 | }, | |||
378 | "nbformat": 4, |
|
402 | "nbformat": 4, | |
379 | "nbformat_minor": 0 |
|
403 | "nbformat_minor": 0 | |
380 | } No newline at end of file |
|
404 | } |
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