Step by step solution to "Evaluate the integral. ∫(x2−2x)dx"

mronjo7n

Answered question

2021-11-20

Evaluate the integral.

\int (x^{2} - 2 x) d x

Vincent Diaz

Beginner2021-11-21Added 19 answers

Step 1
Consider the integrals:

\int (x^{2} - 2 x) d x

Step 2
To solve the given integral:

\int (x^{2} - 2 x) d x = \int x^{2} d x - 2 \int x d x + C

= \frac{x^{2 + 1}}{2 + 1} - 2 \frac{x^{1 + 1}}{1 + 1} + C ∵ \int x^{n} d x = \frac{x^{n + 1}}{n + 1}

= \frac{x^{3}}{3} - \frac{2 x^{2}}{2} + C

= \frac{x^{3}}{3} - x^{2} + C

Tionant

Beginner2021-11-22Added 17 answers

Step 1: Expand.

\int x^{2} - 2 x d x

Step 2: Use Power Rule:

\int x^{n} d x = \frac{x^{n + 1}}{n + 1} + C

\frac{x^{3}}{3} - x^{2}

Step 3: Add constant.

\frac{x^{3}}{3} - x^{2} + C

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