HSC Commerce (English Medium) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions

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)

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

Integrate the following w.r.t.x : `sqrt(x)sec(x^(3/2))*tan(x^(3/2))`

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

Integrate the following w.r.t.x : log (log x)+(log x)^–2 

Integrate the following w.r.t.x : `(1)/(x^3 sqrt(x^2 - 1)`

Integrate the following w.r.t.x : log (x² + 1)

Integrate the following w.r.t.x : e^2x sin x cos x

Integrate the following w.r.t.x : sec⁴x cosec²x

Use quantifiers to convert the following open sentences defined on N, into a true statement.

x² + 3x - 10 = 0