Let

Then

a)

b)

c)

d)

Match

 
for more accurate result for c ε (a, b),
 
when
Find

a)

b)

c)

d)

Let f(x) be a differential function and then

a)

b)

c)

d) 1

If  find  at x = π

Evaluate
  dx

Let A be the area of the region in the first quadrant bounded by the line  , the X–axis and the ellipse  . Find the positive number m such that A is equal to the area of the region in the first quadrant bounded by the line , the Y–axis and the ellipse .

Let I =  and J =  then which of the following is true?

a) I >  and J < 2

b) I >  and J > 2

c) I <  and J < 2

d) I <  and J > 2

a)

b)

c)

d)

The parabola  and  divide the square region bounded by the lines  and the coordinate axes. If  are respectively the area of the parts numbered from top to bottom then  is

a) 1 : 1 :1

b) 2 : 1: 2

c) 1 : 2 : 3

d) 1 : 2 : 1

 is

a) e

b)

c)

d)

Evaluate  

provided not all a, b, c are equal to zero.

Evaluate

Evaluate

Evaluate

Evaluate I =  dx

Evaluate  dx

Evaluate I =

Evaluate I =

Evaluate

Find the anti derivative of the function f : [0, 2] → ℝ

f(x) =  +

For a positive integer n, evaluate

Evaluate