HSC Commerce (English Medium) १२ वीं कक्षा - Maharashtra State Board Important Questions for Mathematics and Statistics

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

State whether the following statement is True or False:

`int sqrt(1 + x^2) *x  "d"x = 1/3(1 + x^2)^(3/2) + "c"`

Evaluate `int (2x + 1)/((x + 1)(x - 2))  "d"x`

`int x/((x - 1)^2 (x + 2)) "d"x`

`int 1/sqrt(x^2 - 9) dx` = ______.

State whether the following statement is true or false.

If `int (4e^x - 25)/(2e^x - 5)` dx = Ax – 3 log |2e^x – 5| + c, where c is the constant of integration, then A = 5.

`int x/((x + 2)(x + 3)) dx` = ______ + `int 3/(x + 3) dx`

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

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

`int 1/sqrt(x^2 - a^2)dx` = ______.