Science (English Medium) इयत्ता १२ - CBSE Important Questions for Mathematics

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"x".tan^-1 "x"  "dx"`

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

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

Prove that `int_0^"a" "f(x)" "dx" = int_0^"a" "f"("a"-"x")"dx"` ,and hence evaluate `int_0^1 "x"^2(1 - "x")^"n""dx"`.

Differentiate `tan^-1[(sqrt(1+"x"^2)-sqrt(1-"x"^2))/(sqrt(1+"x"^2) + sqrt(1-"x"^2))]`with respect to cos⁻¹x².

Integrate the function `cos("x + a")/sin("x + b")` w.r.t. 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 (3x +5)/(x^2+3x-18)dx.`

Evaluate: `int e^x/sqrt(e^(2x) + 4e^x + 13)` dx