HSC Arts (English Medium) इयत्ता १२ वी - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

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)

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

Evaluate the following:

`int (1)/sqrt((x - 3)(x + 2)).dx`

In any ΔABC, prove the following:

`("c" - "b cos A")/("b" - "c cos A") = ("cos B")/("cos C")`