HSC Commerce: Marketing and Salesmanship इयत्ता १२ वी - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

If f'(x) = 4x³ - 3x² + 2x + k, f(0) = 1 and f(1) = 4, find f(x).

Evaluate the following.

`int1/(x^2+4x-5)dx`

Evaluate `int1/(x(x - 1))dx`

Evaluate `int 1/(x(x-1)) dx`

Evaluate `int (5x^2 - 6x + 3)/(2x - 3) dx`

Evaluate the following.

`int1/(x^2 + 4x-5)dx`

If f'(x) = 4x³ – 3x² + 2x + k, f(0) = 1 and f(1) = 4, find f(x).

Evaluate the following.

`int1/(x^2 + 4x - 5)dx`

If f'(x) = 4x³ - 3x² + 2x + k, f(0) = 1 and f(1) = 4, find f(x). 

Evaluate the following.

`intx^3/sqrt(1 + x^4) dx`

Find the rate of change of demand (x) of a commodity with respect to its price (y) if y = 12 + 10x + 25x².

Find the area of the region bounded by the parabola y² = 16x and the line x = 4. 

Evaluate the following : `int x^3.logx.dx`

Choose the correct options from the given alternatives :

`int (1)/(x + x^5)*dx` = f(x) + c, then `int x^4/(x + x^5)*dx` =

Choose the correct options from the given alternatives :

`int (log (3x))/(xlog (9x))*dx` =

Choose the correct options from the given alternatives :

`int (sin^m x)/(cos^(m+2)x)*dx` = 

Choose the correct options from the given alternatives :

`int tan(sin^-1 x)*dx` =

Choose the correct options from the given alternatives :

`int (x- sinx)/(1 - cosx)*dx` =

If f(x) = `sin^-1x/sqrt(1 - x^2), "g"(x) = e^(sin^-1x)`, then `int f(x)*"g"(x)*dx` = ______.

Choose the correct options from the given alternatives :

`int (1)/(cosx - cos^2x)*dx` =