Commerce (English Medium) कक्षा १२ - CBSE Important Questions for Mathematics

Find `int_  (log "x")^2 d"x"`

Prove that `int_a^b ƒ ("x") d"x" = int_a^bƒ(a + b - "x") d"x" and "hence evaluate" int_(π/6)^(π/3) (d"x")/(1+sqrt(tan "x")`

Find the area of the triangle whose vertices are (-1, 1), (0, 5) and (3, 2), using integration. 

Evaluate: `int_-π^π (1 - "x"^2) sin "x" cos^2 "x"  d"x"`.

Evaluate:  `int_-1^2 (|"x"|)/"x"d"x"`.

Find: `int_  (cos"x")/((1 + sin "x") (2+ sin"x")) "dx"`

Evaluate: `int_1^5{|"x"-1|+|"x"-2|+|"x"-3|}d"x"`.

Evaluate: `int_0^pi ("x"sin "x")/(1+ 3cos^2 "x") d"x"`.

Find : `int_  (2"x"+1)/(("x"^2+1)("x"^2+4))d"x"`.

Find: `int_  (3"x"+ 5)sqrt(5 + 4"x"-2"x"^2)d"x"`.

Find: `int sec^2 x /sqrt(tan^2 x+4) dx.`

Find: `intsqrt(1 - sin 2x) dx, pi/4 < x < pi/2`

Find: `int sin^-1 (2x) dx.`

Find: `int logx/(1 + log x)^2 dx`

Evaluate: `int_(-1)^2 |x^3 - 3x^2 + 2x|dx`

If f'(x) = `x + 1/x`, then f(x) is ______.

The value of `int_2^3 x/(x^2 + 1)`dx is ______.

Find: `int (dx)/sqrt(3 - 2x - x^2)`

Evaluate: `int_(pi/6)^(pi/3) (dx)/(1 + sqrt(tanx)`

Find `int (dx)/sqrt(4x - x^2)`