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Find the value of the \(\rm \int_{0}^{2\pi}{sinx}\ dx\)
1. 1
2. 2
3. 0
4. - 1

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Correct Answer - Option 3 : 0

Concept:

  • If f(2a - x) = f(x) then \(\rm \int_{0}^{2a}f(x)dx=2\int_{0}^{a}f(x)dx\)
  • If f(2a - x) = - f(x) then \(\rm \int_{0}^{2a}f(x)dx=0\) 

Calculation:

Given: \(\rm \int_{0}^{2π}{sinx}\ dx\)

Let, f(x) = sin x

As we can see that, f(2π - x) = sin(2π - x) = - sin x

As we know that, if f(2a - x) = - f(x) then\(\rm \int_{0}^{2a}f(x)dx=0\) 

\(\Rightarrow \rm \int_{0}^{2\pi}{sinx}\ dx=0\)

Hence, the correct option is 3.

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