Find the general form of the antiderivative for functions: f (x) = cos ^ 2x-sin ^ 2x.

Find the general form of the antiderivative for functions: f (x) = cos ^ 2x-sin ^ 2x. Prove that the function F is an antiderivative for the function f on the set R: a) F (x) = x ^ 4-3, f (x) = 4x ^ 3;

In order to find the general form of antiderivatives for a function, we transform its equation – we use the formula for finding the cosine of a double angle:

cos 2x = cos ^ 2 x – sin ^ 2 x, which means:

Y = cos 2x;

G = sin 2x * 1/2 + C – general view of antiderivatives for the function Y (C – any number).

2) We have the function F (x) = x ^ 4 – 3;

Find the derivative:

F ‘(x) = 4 * x ^ 3. As you can see, the derivative F ‘(x) is equal to f (x), which means that F (x) is the derivative for f (x).