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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).

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).

Grade:7

1 Answers

Arun Kumar IIT Delhi
askIITians Faculty 256 Points
9 years ago
Ans 1
because limits are same.

We are told to answer only 1 question.



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