Question

Derived by the general formula the following equations remember that you must integrate your procedures

y = 5x -6x² +9x³

Answer 1

Explanation:

The general formula for finding the antiderivative of a polynomial function is to add one to the exponent of each term and divide by that new exponent.

To find the antiderivative of y = 5x -6x² +9x³, we need to integrate each term individually, using the general formula:

∫ (5x) dx = (5/1)x^(1+1) = 5x^2 + C

∫ (-6x²) dx = (-6/2)x^(2+1) = -3x^3 + C

∫ (9x³) dx = (9/4)x^(3+1) = (9/4)x^4 + C

So the antiderivative of y = 5x -6x² +9x³ is:

∫ y dx = 5x^2 - 3x^3 + (9/4)x^4 + C

Where C is the constant of integration, which can take any real value.