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The value of $a$ in $(- π, 0)$ satisfying $\sin α + \int_{α}^{2 α} \cos 2 x d x = 0$ is

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Correct option is C

sin⁡α+∫a2a cos⁡2xdx=0⇒sin⁡α+12(sin⁡4α−sin⁡2α)=0⇒sin⁡α[1+cos⁡(3α)]=0As −π<α<0,sin⁡α≠0 thereforecos⁡(3α)=−1⇒α=−π/3.

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The value of a in (−π,0) satisfying sin⁡α+∫α2α cos⁡2xdx=0 is

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The value of $a$ in $(- π, 0)$ satisfying $\sin α + \int_{α}^{2 α} \cos 2 x d x = 0$ is