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NCERT Class XII Mathematics Chapter - - Solutions

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Exercise - 7.2
Integrate the functions in Exercises 23 to 59.
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Question : 48 of 271
Marks: +1, -0
cos⁡xx\frac{\cos \sqrt{x}}{\sqrt{x}}
Solution:  
Let I=∫cos⁡xx dxI=\int \frac{\cos \sqrt{x}}{\sqrt{x}} \, dx
Put x=t\sqrt{x}=t
⇒12x dx=dt\Rightarrow \frac{1}{2\sqrt{x}} \, dx = dt
∴I=2∫cos⁡t dt\therefore I=2\int \cos t \, dt =2sin⁡t+C=2\sin t + C =2sin⁡x+C=2\sin \sqrt{x} + C
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