Mathematics : Integrals

The number of points having both coordinates as integers that lie in the interior of the triangle with vertices (0,0), (0,41) and (41,0) is

• 901

• 861

• 820

• 820

The integral  dx is equal to 

The Integral  is equal to

• π-4

• 
• 
• 

At present, a firm is manufacturing 2000 items. It is estimated that the rate of change of production P with respect to the additional number of workers x is given by . If the firm employs 25 more workers, then
the new level of production of items is

• 2500

• 3000

• 3500

• 3500

If ∫f x dx =Ψ (x),then ∫x⁵ f(x³)dx is equal to

Statement I - The value of the integral  is equal to π/6.
Statement II-

• Statement -I is True; Statement -II is True; Statement-II is a correct explanation for Statement-I

• Statement - I is True; Statement -II is true; Statement-II is not a correct explanation for Statement-I

• Statement -I is True; Statement -II is False.

• Statement -I is True; Statement -II is False.

If the integral   then an equal to 

• -1

• -2

• 1

• 1

If g(x) =  then g(x +π) equals

• g(x)/g(π)

• g(x) +g(π)

• g (x) - g(π)

• g (x) - g(π)

The value of  is

• 
• 

• log 2

• log 2

The integral  is equal to

• -1

• -2

• 2

• 2