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what is the value of integration of root(x) into sin x . the root is only for x not for sin pls let me know the ans dont think it is a wrong question but it is correct question

what is the value of integration of root(x) into sin x .  the root is only for x not for sin pls let me know the ans dont think it is a wrong question but it is correct question 

Grade:12

2 Answers

Arun
25758 Points
4 years ago
Dear Nikhil,
 
Try with by parts integration
1st is x^(1/2)
2nd is sinx
Now
I = x^(1/2) * (-cosx) - \int(1/2) (1/x^(1/2)) (- cos x) dx
Now again integrate the later part by by parts
You get there is again an algebric fn with sin x
Now take this again as I.
Now you have to give the value of I.
 
Regards
Arun (askIITians forum expert)
Ashish Pandit
13 Points
3 years ago
Dear Nikhil, 
I suppose it should not work.
Because (root x)*(sinx) does have an antiderivative. The solution does not exist.

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