Example 4 Find Fif F X 12x 6x 4 F 0 2 And F 1 9 Solution The General Antiderivative Of F X 12x 6x 1 (40.29 KiB) Viewed 11 times
EXAMPLE 4 Find fif f"(x) = 12x² + 6x-4, f(0) = 2, and f(1) = 9. SOLUTION The general antiderivative of f"(x) = 12x² + 6x - 4 is 3 2 f'(x) = = 12X 3 = f(x) = 4x³ + 3x² - 4x 3 4X Using the antidifferentiation rules once more, we find that 4 we have C = -7 4 + CX + D. = x² + x 3 4 f(x) = x² + x² - +3X -2x² . 3 2 3 + C. + CX + D. - 4x + C To determine C and D we use the given conditions that f(1) = 9. Since f(0) = 0 + D = 2, we have D = 2 f(1) = 1 + 12+ C + 2 = 9 X Therefore, the required function is +³_2x²-7x+2 2 2 f(0) = 2 and ✓ Since
15. [-/1 PUNTOS] MIS NOTAS s(t) = DETALLES SCALCET8 4.9.064. PREGUNTA A TU PROFESOR A particle is moving with the given data. Find the position of the particle. a(t) = ² 2t + 7, s(0) = 0, s(1) = 20 Need Help? PRACTICAR OTRO Read It
OFESOR The acceleration function (in m/s2) and the initial velocity v(0) are given for a particle moving along a line. a(t) = 2t + 2, v(0) = -3, 0 ≤t≤ 3 (a) Find the velocity at time t. v(t) = 1² +2t-3 Need Help? Read It m/s (b) Find the distance traveled during the given time interval. 20/3 X m PRACTICAR OTRO Master It
Join a community of subject matter experts. Register for FREE to view solutions, replies, and use search function. Request answer by replying!