question 2\nfind the most general antiderivative of the function.\n$f(x)=15x^{2}-14x + 8$\n$f(x)=6x^{2}-14x…

question 2\nfind the most general antiderivative of the function.\n$f(x)=15x^{2}-14x + 8$\n$f(x)=6x^{2}-14x + c$\n$f(x)=5x^{3}-7x^{2}+8x + c$\n$f(x)=30x^{5}-28x^{4}+9x + c$\n$f(x)=36x - 14 + c$\n$f(x)=18x^{3}-14x^{2}+9x + c$

question 2\nfind the most general antiderivative of the function.\n$f(x)=15x^{2}-14x + 8$\n$f(x)=6x^{2}-14x + c$\n$f(x)=5x^{3}-7x^{2}+8x + c$\n$f(x)=30x^{5}-28x^{4}+9x + c$\n$f(x)=36x - 14 + c$\n$f(x)=18x^{3}-14x^{2}+9x + c$

Answer

Explanation:

Step1: Apply the power rule for integration

The power rule for integration is (\int x^{n}dx=\frac{x^{n + 1}}{n+1}+C) ((n\neq - 1)). For the function (f(x)=15x^{2}-14x + 8), we integrate each term separately. For the term (15x^{2}): (\int15x^{2}dx=15\times\frac{x^{2+1}}{2 + 1}=15\times\frac{x^{3}}{3}=5x^{3}) For the term (-14x): (\int-14xdx=-14\times\frac{x^{1+1}}{1+1}=-14\times\frac{x^{2}}{2}=-7x^{2}) For the term (8): (\int8dx=8x) (since (\int kdx=kx + C) where (k = 8))

Step2: Combine the integrated terms

Combining the results of the integration of each term, we get (F(x)=5x^{3}-7x^{2}+8x + C)

Answer:

(F(x)=5x^{3}-7x^{2}+8x + C) (the second option)