HSC Science (Computer Science) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions

Integrate the following functions w.r.t. x : `3^(cos^2x) sin 2x`

Integrate the following functions w.r.t. x : `(sin6x)/(sin 10x sin 4x)`

Integrate the following functions w.r.t. x:

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

Evaluate the following : `int (1)/(4x^2 - 3).dx`

Evaluate the following:

`int (1)/(25 - 9x^2)*dx`

Evaluate the following : `int (1)/(7 + 2x^2).dx`

Evaluate the following : `int (1)/sqrt(3x^2 - 8).dx`

Evaluate the following : `int (1)/sqrt(11 - 4x^2).dx`

Evaluate the following : `int (1)/sqrt(2x^2 - 5).dx`

Evaluate the following : `int sqrt((9 + x)/(9 - x)).dx`

Evaluate the following : `int sqrt((2 + x)/(2 - x)).dx`

Evaluate the following : `int sqrt((10 + x)/(10 - x)).dx`

Evaluate the following : `int  (1)/(x^2 + 8x + 12).dx`

Evaluate the following : `int (1)/(1 + x - x^2).dx`

Evaluate the following : `(1)/(4x^2 - 20x + 17)`

Evaluate the following : `int (1)/(5 - 4x - 3x^2).dx`

Evaluate the following : `int (1)/sqrt(3x^2 + 5x + 7).dx`

Solve the triangle in which a = `(sqrt3 + 1)`, b = `(sqrt3 - 1)` and ∠C = 60°.

Evaluate the following : `int (1)/sqrt(x^2 + 8x - 20).dx`

In any Δ ABC, prove the following:

a sin A - b sin B = c sin (A - B)