Question

question 9 - 1 point evaluate the indefinite integral given below. (int(6x^{2}-2x)dx) provide your answer below: (int(6x^{2}-2x)dx=)

Explanation:

Step1: Apply integral sum - difference rule

$\int(6x^{2}-2x)dx=\int6x^{2}dx-\int2xdx$

Step2: Use power - rule for integration $\int x^{n}dx=\frac{x^{n + 1}}{n+1}+C(n

eq - 1)$
For $\int6x^{2}dx$, since $\int kf(x)dx=k\int f(x)dx$ ($k$ is a constant), we have $6\int x^{2}dx=6\times\frac{x^{2 + 1}}{2+1}=2x^{3}$. For $\int2xdx$, $2\int xdx=2\times\frac{x^{1+1}}{1 + 1}=x^{2}$.

Step3: Combine results and add constant of integration

$\int(6x^{2}-2x)dx=2x^{3}-x^{2}+C$

Answer:

$2x^{3}-x^{2}+C$