# Find the value of the $\rm \int_{-\pi }^{\pi }cosx \ dx$

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Find the value of the $\rm \int_{-\pi }^{\pi }cosx \ dx$

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Correct Answer - Option 1 : 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: $\rm \int_{-\pi }^{\pi }cosx \ dx$

Let f(x) = cos x

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

So, cos x is an even function.

As we know that, when f(x) is an even function then $\rm \int_{-a}^{a}f(x)dx=2\int_{0}^{a}f(x)dx$

$\Rightarrow \rm \int_{-\pi }^{\pi }cosx \ dx=2\int_{0 }^{\pi }cosx \ dx=2(sin\pi-sin0)=0$

Hence, the correct option is 1.