Arts (English Medium) Class 12 - CBSE Important Questions

If f(x) = `1/(4x^2 + 2x + 1); x ∈ R`, then find the maximum value of f(x).

Find the maximum profit that a company can make, if the profit function is given by P(x) = 72 + 42x – x², where x is the number of units and P is the profit in rupees.

Check whether the function f : R `rightarrow` R defined by f(x) = x³ + x, has any critical point/s or not ? If yes, then find the point/s.

Evaluate : `int_0^3dx/(9+x^2)`

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

Evaluate: `int(5x-2)/(1+2x+3x^2)dx`

Evaluate : `int_0^4(|x|+|x-2|+|x-4|)dx`

find : `int(3x+1)sqrt(4-3x-2x^2)dx`

Find : `int x^2/(x^4+x^2-2) dx`

Evaluate :`int_0^(pi/2)(2^(sinx))/(2^(sinx)+2^(cosx))dx`

Find:

`int(x^3-1)/(x^3+x)dx`

Find : `int((2x-5)e^(2x))/(2x-3)^3dx`

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

Evaluate `int_(-2)^2x^2/(1+5^x)dx`

Evaluate `int_(-1)^2(e^3x+7x-5)dx` as a limit of sums

Evaluate:

`int x^2/(x^4+x^2-2)dx`

Evaluate:

`int((x+3)e^x)/((x+5)^3)dx`

Find the particular solution of the differential equation x²dy = (2xy + y²) dx, given that y = 1 when x = 1.

find `∫_2^4 x/(x^2 + 1)dx`

Evaluate :   `∫1/(cos^4x+sin^4x)dx`