Arts (English Medium) Class 12 - CBSE Question Bank Solutions for Mathematics

Integrate the rational function:

`((x^2 +1)(x^2 + 2))/((x^2 + 3)(x^2+ 4))`

Integrate the rational function:

`(2x)/((x^2 + 1)(x^2 + 3))`

Integrate the rational function:

`1/(x(x^4 - 1))`

Integrate the rational function:

`1/(e^x -1)`[Hint: Put e^x = t]

`int (xdx)/((x - 1)(x - 2))` equals:

`int (dx)/(x(x^2 + 1))` equals:

Using properties of determinants, prove that 

`|(a^2 + 2a,2a + 1,1),(2a+1,a+2, 1),(3, 3, 1)| = (a - 1)^3`

Find `int(e^x dx)/((e^x - 1)^2 (e^x + 2))`

Using properties of determinants, prove that `|(x,x+y,x+2y),(x+2y, x,x+y),(x+y, x+2y, x)| = 9y^2(x + y)`

Find the particular solution of the differential equation e^x tan y dx + (2 – e^x) sec² y dy = 0, give that `y = pi/4` when x = 0

Find the particular solution of the differential equation `dy/dx + 2y tan x = sin x` given that y = 0 when x =  `pi/3`

Using properties of determinants, prove that `|(1,1,1+3x),(1+3y, 1,1),(1,1+3z,1)| = 9(3xyz + xy +  yz+ zx)`

Find `int (2cos x)/((1-sinx)(1+sin^2 x)) dx`

f(x) = 4x² + 4 on R .

f(x)=| x+2 | on R .

f (x) = \[-\] | x + 1 | + 3 on R .