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@@ -37,7 +37,7 b'' | |||
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37 | 37 | "cell_type": "code", |
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38 | 38 | "execution_count": 2, |
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39 | 39 | "metadata": { |
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40 |
"collapsed": |
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40 | "collapsed": false | |
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41 | 41 | }, |
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42 | 42 | "outputs": [], |
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43 | 43 | "source": [ |
@@ -63,9 +63,10 b'' | |||
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63 | 63 | }, |
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64 | 64 | "outputs": [], |
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65 | 65 | "source": [ |
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66 | "a, b = 1, 9\n", | |
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67 | "xint = x[np.logical_and(x>=a, x<=b)][::30]\n", | |
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68 | "yint = y[np.logical_and(x>=a, x<=b)][::30]" | |
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66 | "a, b = 1, 8 # the left and right boundaries\n", | |
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67 | "N = 5 # the number of points\n", | |
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68 | "xint = np.linspace(a, b, N)\n", | |
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69 | "yint = f(xint)" | |
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69 | 70 | ] |
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70 | 71 | }, |
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71 | 72 | { |
@@ -85,250 +86,255 b'' | |||
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85 | 86 | { |
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86 | 87 | "data": { |
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87 | 88 | "image/png": [ |
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329 | "38jXAc8M4v2HDBER4DfARmPMT52OB0BEUkQkwX7vBS7E6tt3jDHmX4wxOcaYMVhf2f9kjLnFyZhE\n", | |
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331 | "+BOye6q/13LpkgnDSUci8igwH0gWkX3At40xK52MyTYba2OPj0TkQ/vYncaYFx2MKRN4wF4i2QU8\n", | |
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332 | "box53sF4QgmHbr104A9WLiACeNgY87KzIQHwt8DDdmNqB7DC4XiAT3/pLeLUNpOOMsa8KyKrsNaP\n", | |
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333 | "arNff+1sVACsEpFkoBW43RhzIlQlnViklFLDxFDYgk4ppVQPaEJXSqlhQhO6UkoNE5rQlVJqmNCE\n", | |
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334 | "rpRSw4QmdKWUGiY0oSul1DChCV0ppYaJ/w8u1j+cuZEJ1QAAAABJRU5ErkJggg==\n" | |
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329 | 335 | ], |
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330 | 336 | "text/plain": [ |
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331 |
"<matplotlib.figure.Figure at 0x |
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337 | "<matplotlib.figure.Figure at 0x7f47175e3898>" | |
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332 | 338 | ] |
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333 | 339 | }, |
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334 | 340 | "metadata": {}, |
@@ -337,7 +343,7 b'' | |||
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337 | 343 | ], |
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338 | 344 | "source": [ |
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339 | 345 | "plt.plot(x, y, lw=2)\n", |
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340 |
"plt.axis([0, |
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346 | "plt.axis([0, 9, 0, 140])\n", | |
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341 | 347 | "plt.fill_between(xint, 0, yint, facecolor='gray', alpha=0.4)\n", |
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342 | 348 | "plt.text(0.5 * (a + b), 30,r\"$\\int_a^b f(x)dx$\", horizontalalignment='center', fontsize=20);" |
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343 | 349 | ] |
@@ -360,21 +366,39 b'' | |||
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360 | 366 | "name": "stdout", |
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361 | 367 | "output_type": "stream", |
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362 | 368 | "text": [ |
|
363 |
"The integral is: |
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364 |
"The trapezoid approximation with |
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369 | "The integral is: 565.2499999999999 +/- 6.275535646693696e-12\n", | |
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370 | "The trapezoid approximation with 5 points is: 559.890625\n" | |
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365 | 371 | ] |
|
366 | 372 | } |
|
367 | 373 | ], |
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368 | 374 | "source": [ |
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369 | 375 | "from __future__ import print_function\n", |
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370 |
"from scipy.integrate import quad |
|
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371 |
"integral, error = quad(f, |
|
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376 | "from scipy.integrate import quad\n", | |
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377 | "integral, error = quad(f, a, b)\n", | |
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378 | "integral_trapezoid = sum( (xint[1:] - xint[:-1]) * (yint[1:] + yint[:-1]) ) / 2\n", | |
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372 | 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)" | |
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374 | 381 | ] |
|
375 | 382 | } |
|
376 | 383 | ], |
|
377 |
"metadata": { |
|
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384 | "metadata": { | |
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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 | 402 | "nbformat": 4, |
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379 | 403 | "nbformat_minor": 0 |
|
380 | 404 | } No newline at end of file |
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