Question

Даю 100 балов
Помогите

Answer 1

F'(x) = f(x)

f(x) = 4x³

$1) F(x) = \int {4x^{3}} \, dx = 4\int {x^{3}} \, dx = 4 * \frac{x^{4}}{4} + C = x^{4} + C$

$F(1) = -1 = > 1 + C = -1 = > C = -2 = > F(x) = x^4 - 2$

$F(2) = 2^{4} - 2 = 16 - 2 = 14$

$2) \int\limits^3_2 {f(x)} \, dx = \int\limits^3_2 {4x^{3}} \, dx = 4\int\limits^3_2 {x^{3}} \, dx = x^{4} (2|3) = 3^{4} - 2^{4} = 81 - 16 = 65$