Science (English Medium) इयत्ता १२ - CBSE Important Questions

Evaluate each of the following integral:

Find : `∫_a^b logx/x` dx

Find : 

`∫ sin(x-a)/sin(x+a)dx`

Find : 

`∫(log x)^2 dx`

Prove that `int _a^b f(x) dx = int_a^b f (a + b -x ) dx`  and hence evaluate   `int_(pi/6)^(pi/3) (dx)/(1 + sqrt(tan x))` .   

Find `int_  (sin "x" - cos "x" )/sqrt(1 + sin 2"x") d"x", 0 < "x" < π / 2 `

Find `int_  sin ("x" - a)/(sin ("x" + a )) d"x"`

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"dx"/sqrt(5-4"x" - 2"x"^2)`

Find:
`int_(-pi/4)^0 (1+tan"x")/(1-tan"x") "dx"`