If $$I=$$∫$$0$$$$π$$$$2$$ $$cos$$⁡$$($$$$sin$$⁡$$x)dx$$,$$J=$$∫$$0$$$$π$$$$2$$ $$sin$$⁡$$($$$$cos$$⁡$$x)dx$$ and $$K=$$∫$$0$$$$π$$$$2$$ $$cos$$⁡xdx, then

Question

If $$I=$$∫$$0$$$$π$$$$2$$ $$cos$$⁡$$($$$$sin$$⁡$$x)dx$$,$$J=$$∫$$0$$$$π$$$$2$$ $$sin$$⁡$$($$$$cos$$⁡$$x)dx$$ and $$K=$$∫$$0$$$$π$$$$2$$ $$cos$$⁡xdx, then

Infinity Learn · Accepted Answer

Given that $$I=$$∫$$0$$$$π$$$$2$$ $$cos$$⁡$$($$$$sin$$⁡$$x)dx$$,$$J=$$∫$$0$$$$π$$$$2$$ $$sin$$⁡$$($$$$cos$$⁡$$x)dx$$,$$k=$$∫$$0$$$$π$$$$2$$ $$cos$$⁡xdx We know that $$cos$$⁡$$($$$$sin$$⁡$$x)$$>$$cos$$⁡x>$$sin$$⁡$$($$$$cos$$⁡$$x)$$ for x∈$$0$$,π$$2$$ since sinx cosx     since $$cos$$ function is decreasing $$in0$$,π$$2$$                                                                                                                                                                                                                        ⇒∫$$0$$$$π$$$$2$$ $$cos$$⁡$$($$$$sin$$⁡$$x)dx$$>∫$$0$$$$π$$$$2$$ $$cos$$⁡xdx>∫$$0$$$$π$$$$2$$ $$sin$$⁡$$($$$$cos$$⁡$$x)dx$$⇒I>K>J

$If I = \int_{0}^{\frac{π}{2}} \cos (\sin x) d x, J = \int_{0}^{\frac{π}{2}} \sin (\cos x) d x and K = \int_{0}^{\frac{π}{2}} \cos x d x, then$

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

If I=∫0π2 cos⁡(sin⁡x)dx,J=∫0π2 sin⁡(cos⁡x)dx and K=∫0π2 cos⁡xdx, then

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

$If I = \int_{0}^{\frac{π}{2}} \cos (\sin x) d x, J = \int_{0}^{\frac{π}{2}} \sin (\cos x) d x and K = \int_{0}^{\frac{π}{2}} \cos x d x, then$