Commerce (English Medium) Class 12 - CBSE Question Bank Solutions for Mathematics

Evaluate the following:

`int_0^(pi/2)  "dx"/(("a"^2 cos^2x + "b"^2 sin^2 x)^2` (Hint: Divide Numerator and Denominator by cos⁴x)

Evaluate the following:

`int_(-pi/4)^(pi/4) log|sinx + cosx|"d"x`

`int_((-pi)/4)^(pi/4) "dx"/(1 + cos2x)` is equal to ______.

`int_0^(pi/2) sqrt(1 - sin2x)  "d"x` is equal to ______.

`int_0^(pi/2)  cos x "e"^(sinx)  "d"x` is equal to ______.

If `int_0^"a" 1/(1 + 4x^2) "d"x = pi/8`, then a = ______.

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

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_0^(2π) (1)/(1 + e^(sin x)`dx

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

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

Evaluate `int_0^(π//4) log (1 + tanx)dx`.

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

If `int_0^(2π) cos^2 x  dx = k int_0^(π/2) cos^2 x  dx`, then the value of k is ______.

`int_-1^1 |x - 2|/(x - 2) dx`, x ≠ 2 is equal to ______.

Assertion (A): `int_2^8 sqrt(10 - x)/(sqrt(x) + sqrt(10 - x))dx` = 3.

Reason (R): `int_a^b f(x) dx = int_a^b f(a + b - x) dx`.

The value of `int_0^(π/4) (sin 2x)dx` is ______.

Evaluate: `int_(-π//4)^(π//4) (cos 2x)/(1 + cos 2x)dx`.

Evaluate: `int_0^π x/(1 + sinx)dx`.