Integrallar jadvali va sodda qoidalar
Javoblar ota-onalar va o‘qituvchilar uchun.
1
∫ (8x³ − 5x + 2/x) dx (x > 0) ni hisoblang.
2x⁴ − 5x²/2 + 2 ln x + C.
2
∫ (cos 3x − 4 sin(2x + 1)) dx ni toping.
(1/3) sin 3x + 2 cos(2x + 1) + C.
3
∫ x²/(x³ + 1) dx (x > −1) ni o‘zgaruvchini almashtirib toping.
u = x³ + 1, x² dx = du/3: (1/3) ln(x³ + 1) + C.
4
sin²x = (1 − cos 2x)/2 dan foydalanib, ∫ sin²x dx ni hisoblang va javobni differensiallab tekshiring.
x/2 − (sin 2x)/4 + C; hosila: 1/2 − cos 2x/2 = sin²x.
5
f(x) = e^x + 2x ning grafigi (0; 3) nuqtadan o‘tuvchi boshlang‘ich funksiyasini toping.
F = eˣ + x² + C; 1 + C = 3 ⇒ C = 2; F = eˣ + x² + 2.