A) \[\sin \sqrt{x}-\sqrt{x}\,\cos \,\sqrt{x}\]
B) \[2(\sin \,\sqrt{x}-\sqrt{x}\,\cos \,\sqrt{x})+c\]
C) \[\cos \,\sqrt{x}-\sqrt{x}\,\sin \,\sqrt{x}+c\]
D) \[2(\cos \sqrt{x}-\sqrt{x}\,\sin \sqrt{x})+c\]
Correct Answer: B
Solution :
Let \[I=\int{\sin \,\sqrt{x}}\,dx\] Put \[\sqrt{x}=t\,\,\,\,\Rightarrow \,\,\frac{1}{2\sqrt{x}}\,dx=dt\] \[\therefore \] \[I=\int{2t\,\sin \,t\,dt}\] \[=2[-t\,\cos \,\,t+\int{\cos \,t\,dt}]\] \[=2[-t\,\cos \,t+\sin \,t]+c\] \[=2[-\sqrt{x}\,\cos \,\sqrt{x}+\sin \,\sqrt{x}]+c\]
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