HSC Commerce (English Medium) १२ वीं कक्षा - Maharashtra State Board Question Bank Solutions

`int (f^'(x))/(f(x))dx` = ______ + c.

`int(7x - 2)^2dx = (7x -2)^3/21 + c`

Find the value of x for which the function f(x)= 2x³ – 9x² + 12x + 2 is decreasing.

Given f(x) = 2x³ – 9x² + 12x + 2

∴ f'(x) = `squarex^2 - square + square`

∴ f'(x) = `6(x - 1)(square)`

Now f'(x) < 0

∴ 6(x – 1)(x – 2) < 0

Since ab < 0 ⇔a < 0 and b < 0 or a > 0 and b < 0

Case 1: (x – 1) < 0 and (x – 2) < 0

∴ x < `square` and x > `square`

Which is contradiction

Case 2: x – 1 and x – 2 < 0

∴ x > `square` and x < `square`

1 < `square` < 2

f(x) is decreasing if and only if x ∈ `square`

If b_xy < 0 and b_yx < 0 then 'r ' is ______.

A function f is said to be increasing at a point c if ______.

The degree of the differential equation `((d^2y)/dx^2)^2 + (dy/dx)^3` = a^x is 3.

Converse of the statement q `rightarrow` p is ______.

`int(1 - x)^(-2)` dx = `(1 - x)^(-1) + c`

Evaluate `int(1 + x + x^2/(2!) )dx`

Evaluated the following

`int x^3/ sqrt (1 + x^4 )dx`

Evaluate `int (1+x+x^2/(2!))dx`

Evaluate the following.

`int x^3/(sqrt(1+x^4))dx`

Evaluate `int(1+ x + x^2/(2!)) dx`

Evaluate the following.

`int(20 - 12"e"^"x")/(3"e"^"x" - 4) "dx"`

if `f(x) = 4x^3 - 3x^2 + 2x +k, f (0) = - 1 and f (1) = 4, "find " f(x)`

If f′(x) = 4x³ − 3x² + 2x + k, f(0) = -1 and f(1) = 4, find f(x)

Evaluate the following.

`int 1/(x^2+4x-5)  dx`

Evaluate the following

`int1/(x^2 +4x-5)dx`

Evaluate `int 1/("x"("x" - 1)) "dx"`

Evaluate.

`int(5"x"^2 - 6"x" + 3)/(2"x" - 3)  "dx"`