HSC Commerce (English Medium) 12th Standard Board Exam - Maharashtra State Board Important Questions

Integrate the following w.r.t. x : `((3sin - 2)*cosx)/(5 - 4sin x - cos^2x)`

Evaluate the following.

`int 1/(x(x^6 + 1))` dx 

Evaluate the following.

`int 1/(4x^2 - 20x + 17)` dx

Evaluate the following.

`int x/(4x^4 - 20x^2 - 3) dx`

Evaluate the following.

`int 1/(7 + 6"x" - "x"^2)` dx

Evaluate the following.

`int x^2 *e^(3x)`dx

Evaluate:

`int (2x + 1)/(x(x - 1)(x - 4)) dx`.

Evaluate:

`int x/((x - 1)^2(x + 2)) dx`

`int "dx"/(("x" - 8)("x" + 7))`=

If f '(x) = `1/"x" + "x"` and f(1) = `5/2`, then f(x) = log x + `"x"^2/2` + ______

To find the value of `int ((1 + log x) )/x dx` the proper substitution is ______.

For `int ("x - 1")/("x + 1")^3  "e"^"x" "dx" = "e"^"x"` f(x) + c, f(x) = (x + 1)².

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

Evaluate:

∫ (log x)² dx

Choose the correct alternative:

`int(("e"^(2x) + "e"^(-2x))/"e"^x) "d"x` =

`int (5(x^6 + 1))/(x^2 + 1) "d"x` = x⁵ – ______ x³ + 5x + c

`int (x^2 + x - 6)/((x - 2)(x - 1))  "d"x` = x + ______ + c

State whether the following statement is True or False:

If `int x  "f"(x) "d"x = ("f"(x))/2`, then f(x) = `"e"^(x^2)`

State whether the following statement is True or False:

If `int((x - 1)"d"x)/((x + 1)(x - 2))` = A log|x + 1|  + B log|x – 2|, then A + B = 1

State whether the following statement is True or False:

For `int (x - 1)/(x + 1)^3  "e"^x"d"x` = e^x f(x) + c, f(x) = (x + 1)²