HSC Commerce (English Medium) १२ वीं कक्षा - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

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` =

Choose the correct options from the given alternatives :

`int sin (log x)*dx` =

Choose the correct options from the given alternatives :

`int cos -(3)/(7)x*sin -(11)/(7)x*dx` =

Choose the correct options from the given alternatives :

`int [sin (log x) + cos (log x)]*dx` =

Integrate the following with respect to the respective variable : `t^3/(t + 1)^2`

Integrate the following with respect to the respective variable : `(3 - 2sinx)/(cos^2x)`

Integrate the following with respect to the respective variable : `(sin^6θ + cos^6θ)/(sin^2θ*cos^2θ)`

Integrate the following with respect to the respective variable : cos 3x cos 2x cos x

Integrate the following w.r.t. x: `(1 + log x)^2/x`

Integrate the following w.r.t.x : cot^–1 (1 – x + x²)