Find the value of the $\rm \int_{-5 }^5 5x \ dx$

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Find the value of the $\rm \int_{-5 }^5 5x \ dx$
1. - 1
2. 2
3. 1
4. 0

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Correct Answer - Option 4 : 0

Concept:

The function f(x) is an odd function if f(x) = - f(-x) and an even function if f(x) = f(-x).

• When f(x) is an even function then $\rm \int_{-a}^{a}f(x)dx=2\int_{0}^{a}f(x)dx$
• When f(x) is odd function then $\rm \int_{-a}^{a}f(x)dx=0$
Calculation:

Given: $\rm \int_{-5 }^5 5x \ dx$

Let f(x) = 5x

As we can see that, f(- x) = 5(- x) = - 5x = - f(x).

So, f(x) = 5x is an odd function.

As we know that, when f(x) is an odd function then $\rm \int_{-a}^{a}f(x)dx=0$

$\Rightarrow\rm \int_{-5 }^5 5x \ dx=0$

Hence, the correct option is 4.