Prob 1
If f (x) =intigral
upper limit is x power 2
and lower limit is 1/x square
root of sin( t)dt, then find the value of f (1).
Prob 2
Let a = min x2 + 4x + 5, x ? R and
b = lim??0 1-cos 2?/?square
then find the value of
a-b
a+b .
Prob 3
The value of the Integral
upper limit is p/2
lower limit is -p/2
(ax^3cos x + b sin x + c)dx, depends on how many parameters among (a , b , c).
Prob 4
Find the value of the Integral
upper limit is p/2
lower limit is -p/2
root of ( cos x - cos^3 x)dx.
Prob 5
Let f (x) =integral
upper limit is x
lower limit is 0
( 2u+1/u^2-2u+2 )du then find the least value of f (x) in [-1,1].
Prob 6
Find the values of a for which the function f (x) = cos x - sin x + ax + b is decreasing.
Prob 7
Find the area bounded by the curves y=x|x| , x - axis , x = 1 & x = -1.
Prob 8
For x > 0 let f (x) =integral
upper limit is x
lower limit is 1
ln(t)/1+t,
Find the function f (x) + f (1/x) and show that f (e) + f (1/e) = 1/2.
Prob 9
Is the function f (x) = |x^2 - x| differentiable at x = 2. If yes find it’s derivative.
Prob 10
Check the monotonicity of f (x) =x/sinx
in (0, p/2).
Pushkar Aditya , 12 Years ago
Grade 7
