Find the antiderivative of the function f(x) = 3x^2 + 4x - 5.
To find the antiderivative of the function f(x) = 3x^2 + 4x - 5, we need to find a function F(x) whose derivative is equal to f(x).
Let's find the antiderivative term by term:
The antiderivative of 3x^2 will be obtained by adding 1 to the exponent and dividing by the new exponent, resulting in (3/3)x^3 = x^3.
The antiderivative of 4x will be obtained by adding 1 to the exponent and dividing by the new exponent, resulting in (4/2)x^2 = 2x^2.
The antiderivative of -5 will be obtained by multiplying the constant by x and then the antiderivative of x^0 is x. So, -5 * x = -5x.
Putting it all together, the antiderivative F(x) of f(x) = 3x^2 + 4x - 5 is given by:
F(x) = x^3 + 2x^2 - 5x + C,
where C is the constant of integration.
Therefore, the antiderivative of f(x) = 3x^2 + 4x - 5 is F(x) = x^3 + 2x^2 - 5x + C.