The value of the definite integral ∫−$$1212$$ $$sin$$−$$1$$⁡$$3x$$−$$4x3$$−$$cos$$−$$1$$⁡$$4x3$$−$$3xdx=$$

Question

The value of the definite integral ∫−$$1212$$ $$sin$$−$$1$$⁡$$3x$$−$$4x3$$−$$cos$$−$$1$$⁡$$4x3$$−$$3xdx=$$

Infinity Learn · Accepted Answer

For x∈−$$12$$,$$12$$,$$sin$$−$$1$$⁡$$3x$$−$$4x3=3sin$$−$$1$$⁡x and                           $$cos$$−$$1$$⁡$$4x3$$−$$3x=2$$π−$$3cos$$−$$1$$⁡x Let $$I=$$∫−$$1212$$ $$sin$$−$$1$$⁡$$3x$$−$$4x3$$−$$cos$$−$$1$$⁡$$4x3$$−$$3xdx=$$∫−$$1212$$ $$3sin$$−$$1$$⁡x−$$2$$π$$+3cos$$−$$1$$⁡xdx $$=$$∫−$$1212$$ $$3$$$$π$$$$2$$−$$2$$$$π$$$$dx=$$−π$$2$$ $$12--12$$  $$=$$ −π$$2$$           since $$sin$$$$-1x+$$$$cos$$$$-1x=$$π$$2$$

$The value of the definite integral \int_{- \frac{1}{2}}^{\frac{1}{2}} (\sin^{- 1} (3 x - 4 x^{3}) - \cos^{- 1} (4 x^{3} - 3 x)) d x =$

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The value of the definite integral ∫−1212 sin−1⁡3x−4x3−cos−1⁡4x3−3xdx=

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$The value of the definite integral \int_{- \frac{1}{2}}^{\frac{1}{2}} (\sin^{- 1} (3 x - 4 x^{3}) - \cos^{- 1} (4 x^{3} - 3 x)) d x =$