Question

Evaluate the following integrals:∫x2−2​dx

Answer 1

Appropriate Question:

Evaluate the following integral,

$\displaystyle\int x^2 - 2\ dx$

Solution:

We have,

${\displaystyle\rm I = \int x^2 - 2\ dx}$

Applying linearity, we have:

${\displaystyle\rm I = \int x^2 \ dx - 2\int\ dx}$

Now, we will use the following power rule,

$\boxed{\tt \int x^n \ dx = \dfrac{x^{n+1}}{n+1} + C}$

Using this formula, our integral changes to,

${\displaystyle\rm I = \dfrac{x^{2+1}}{2+1} + C_1 - 2x + C_2}$

${\displaystyle\rm I = \dfrac{1}{3}x^3 - 2x +( C_1 + C_2)}$

${\displaystyle\rm I = \dfrac{1}{3}x^3 - 2x +C}$

So the required answer is,

$\boxed{\int x^2 - 2 \ dx = \dfrac{1}{3} x^3 - 2x + C}$

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