Question

integration x^2019 DX limit 2 to-2​

Answer 1

Given : integration of x^2019 dx limits 2 to -2

$\int\limits^2_{-2} {x^{2019}} \, dx$

complete Question: https://brainly.in/question/28475739

To Find :  Value

1). 0

2). 2020

3). 4

4). 4040​

Solution:

integration of any odd function over a symmetric interval is always zero

f(x) = x²⁰¹⁹

f(-x) = (-x)²⁰¹⁹ = -  x²⁰¹⁹  = - f(x)

f(-x) = -f(x)

Hence f(x) is odd function

Interval is -2 to 2

-2 to 0  and 0 to 2

Hence symmetric interval

so Integration is Zero

Correct option is option 1)  0

$\int\limits^2_{-2} {x^{2019}} \, dx$

$=\left \dfrac{x^{2020}}{2020} \right|_{-2}^2$

= 2²⁰²⁰/2020  -  (-2)²⁰²⁰/2020

= 2²⁰²⁰/2020  -  (2)²⁰²⁰/2020

= 0

Hence Correct option is option 1)  0

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