Science (English Medium) Class 12 - CBSE Important Questions

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"`.

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.`

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

Find: `int e^x.sin2xdx`

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

Evaluate: `int_0^(π/2) 1/(1 + (tanx)^(2/3)) dx`

Evaluate: `int_1^3 sqrt(x)/(sqrt(x) + sqrt(4) - x) dx`

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

Evaluate: `int_((-π)/2)^(π/2) (sin|x| + cos|x|)dx`

Evaluate `int_-1^1 |x^4 - x|dx`.