Evaluate   dx,  a>0

a) 2π

b)

c)

d) aπ

If  dx =Ax + B ln sin(x

Then value of (A, B) is

a) (sinα, cosα)

b) (cosα, sinα)

c) (sinα, cosα)

d) (cosα, sinα)

 =

a)  ln  + c

b)  ln  + c

c)  ln  + c

d)  ln  + c

a)

b)

c)

d)

If   

then A is equal to

a) 0

b)

c)

d)

If

Then the value of  is

a) 2

b)  

c)  

d)  

If  and   then

a)

b)

c)

d)

If  then  is equal to

a)

b)

c)

d)

The value of the integral is

a)

b)

c)

d)

Let  If  then

one of the possible values of k is

a) 15

b) 16

c) 63

d) 64

Let  be a function satisfying  with  and  be a function that satisfies  then the value of the integral  is

a)

b)

c)

d)

 is

a) 20

b) 8

c) 10

d) 18

, then  equals

a)

b) 1

c)

d) 0

dx is

a)

b)

c)

d)

Evaluate  dx

a)

b)

c) 0

d) 1

a)

b)

c)

d) None of the above

Let f(x) be differentiable for all x. If f (1) = − 2 and  for x [1, 6] then

a) f(6)=5

b) f(6) < 5

c) f(6) < 8

d) f(6) ≥ 8

The value of the definite integral  is

a) – 1

b) 2

c)

d)

The area bounded by the curve y = f(x), the X–axis and the ordinate x = 1 and x = b is (b – 1) sin (3b + 4). Then f(x) is

a) (x – 1) cos (3x + 4)

b) sin(3x + 4)

c) sin(3x + 4) + 3(x – 1) cos (3x + 4)

d) none of these

The slope of the tangent to the curve y = f(x) at [x, f(x)] is 2x + 1. The curve passes through (1, 2), then the area bounded by the curve and X–axis, and the line x = 1 is

a)

b)

c)

d) 6

Let   then the real roots of the equation

 are

a) ± 1

b)

c)

d) 0 and 1

The area bounded by the curves  

and the X–axis in the first quadrant is

a) 9

b)

c) 36

d) 18

The area enclosed between y = ax² and x = ay² (a > 0)

is one square unit. Then the value of a is

a)

b)

c) 1

d)