Methods of integration
Change the variable and the limits together, integrate by parts, split a fraction into partial fractions, pick a trigonometric substitution and decide whether an improper integral has a value.
- فلسطين: الصف ١٢
- إيران: الصف ١٢
- أفغانستان: الصف ١٢
- روسيا: الصف ١١
- ألمانيا: الصف ١٢
- فرنسا: الصف ١٢
- بريطانيا: السنة ١٢
لم يُترجَم هذا المختبر إلى هذه اللغة بعد.
الدليل
التكامل بتغيير المتحول: write u for the inside part, replace dx using du, and for a definite integral change the limits to u-values too. Then you never need to go back to x.
المكاملة بالتجزئة: ∫udv = uv − ∫vdu. Choose u as the part that gets simpler when differentiated (x), and dv as the part you can integrate (eˣ dx). كسور جزئية: a fraction with a factorised denominator is split into simple fractions, each easy to integrate.
For √(1 − x²) the substitution x = sin θ turns the root into cos θ. An improper integral has an infinite limit (or an infinite value of f): it is a limit, and it may converge to a number or diverge.