+91-87964 74404
FlagBACK
Question icon
Integral Calculus

integrating from sin x to 1 (t^2f(t)dt=i-sinx for all x E R.THEN F(1/SQ.RT(3)) IS

Profile image of ZZZ ZZZ
15 Years agoGrade
Answers icon

1 Answer

Profile image of Jitender Singh
12 Years ago
Ans:
\int_{sinx}^{1}t^{2}f(t)dt = i - sinx
Differentiating both sides. Integral will be differentiated by Leibniz integral rule,
(1)^{2}f(1)\frac{\partial (1)}{\partial x}-(sinx)^{2}f(sinx)\frac{\partial (sinx)}{\partial x}+\int_{1}^{sinx}\frac{\partial (t^{2}f(t))}{\partial x}dx = -cosx
-sin^{2}x.(f(sinx)).cosx + 0 = -cosx
(f(sinx)) = \frac{1}{sin^{2}x}
f(\frac{1}{\sqrt{3}}) = \frac{1}{(\frac{1}{\sqrt{3}})^{2}}
f(\frac{1}{\sqrt{3}}) = 3
Thanks & Regards
Jitender Singh
IIT Delhi
askIITians Faculty

Other Related Questions on integral calculus

question mark
The area of a square field is 640000cm2.what is its area in hectares
integral calculus
1 Answer Available

Last Activity: 3 Years ago

question mark
Please solve this integration. I am facing difficulty in it
 How to solve this. Please solve anyone. Humble request
integral calculus
1 Answer Available

Last Activity: 4 Years ago

question mark
Using laplace transform, solve d2y/dt2 + dy/dt = t2 +2t given that y=4 and y’=-2 and t=0
integral calculus
1 Answer Available

Last Activity: 4 Years ago

question mark
If 4th term of an A.p is zero, show that the 8th term is double the 6th term
 
integral calculus
1 Answer Available

Last Activity: 4 Years ago