HSC Arts इयत्ता ११ - Tamil Nadu Board of Secondary Education Question Bank Solutions

Choose the correct alternative:

`int 2^(3x + 5)  "d"x` is

Choose the correct alternative:

`int ("e"^x(x^2 tan^-1x + tan^-1x + 1))/(x^2 + 1)  "d"x` is

Choose the correct alternative:

`int (x^2 + cos^2x)/(x^2 + 1)  "cosec"^2 x/("d"x)` is

Choose the correct alternative:

`int x^2 cos x  "d"x` is

Choose the correct alternative:

`int sqrt((1 - x)/(1 + x))  "d"x` is

Choose the correct alternative:

`int ("d"x)/("e"^x - 1)` is

Choose the correct alternative:

`int "e"^(- 4x) cos   "d"x` is

Choose the correct alternative:

`int (sec^2x)/(tan^2 x - 1)  "d"x`

Choose the correct alternative:

`int "e"^(- 7x) sin 5x  "d"x` is

Choose the correct alternative:

`int x^2 "e"^(x/2)  "d"x` is

Choose the correct alternative:

`int (x + 2)/sqrt(x^2 - 1)  "d"x` is

Choose the correct alternative:

`int 1/(x sqrt(log x)^2 - 5)  "d"x` is

Choose the correct alternative:

`int sin sqrt(x)  "d"x` is

Choose the correct alternative:

`int "e"^(sqrt(x)) "d"x` is

Find the principal value of the following:

`sin^-1 (- 1/2)`

Find the principal value of the following:

tan^-1 (-1)

Find the principal value of the following:

cosec^-1 (2)

Find the principal value of the following:

`sec^-1 (-sqrt2)`

Prove that:

2 tan^-1 (x) = `sin^-1 ((2x)/(1 + x^2))`

Prove that:

`tan^-1 (4/3) + tan^-1 (1/7) = pi/4`