Derivatives

Since

%5Cint_%7Bsin%20x%7D%5E1%20%5C%2C%20t%5E2%20f(t)%20dt%20%3D1-sin%20x

thus to find f(x)
On differentiating both sides using Newton Leibnitz
formula
i.e.

%5Chspace%7B20mm%7D%20%5Cfrac%7Bd%7D%7Bdx%7D%20%5Cint_%7Bsin%20x%7D%5E1%20t%5E2%20f(t)%20dt%20%3D%5Cfrac%7Bd%7D%7Bdx%7D(1-sin%20x)

%5CRightarrow%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%7B%201%5E2f(-1)%5C%7D.(0)-(sin%5E2x).f(sin%20x).cos%20x%3D-cos%20x

%5CRightarrow%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5Chspace%7B20mm%7D%20f(sin%20x)%3D%5Cfrac%7B1%7D%7Bsin%5E2%20x%7D

For f

%5Cbigg(%5Cfrac%7B1%7D%7B%5Csqrt%203%7D%5Cbigg)

is obtained when sin x =

1%5Csqrt%203

i.e

%5Chspace%7B20mm%7D%20f%5Cbigg(%5Cfrac%7B1%7D%7B%5Csqrt%203%7D%5Cbigg)%20%3D(%5Csqrt%203)%5E2%20%3D3

Chapter Questions
1 MCQs