HSC Commerce (English Medium) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions

Evaluate the following.

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

Evaluate the following.

`int 1/(sqrt(3"x"^2 + 8))` dx

Evaluate the following.

`int 1/(sqrt("x"^2 + 4"x"+ 29))` dx

Evaluate the following.

`int 1/(sqrt(3"x"^2 - 5))` dx

Evaluate the following.

`int 1/(sqrt("x"^2 -8"x" - 20))` dx

Choose the correct alternative from the following.

The value of `int "dx"/sqrt"1 - x"` is

`int sqrt(1 + "x"^2) "dx"` =

Choose the correct alternative from the following.

`int "x"^2 (3)^("x"^3) "dx"` =

`int ("x + 2")/(2"x"^2 + 6"x" + 5)"dx" = "p" int (4"x" + 6)/(2"x"^2 + 6"x" + 5) "dx" + 1/2 int "dx"/(2"x"^2 + 6"x" + 5)`, then p = ?

Choose the correct alternative from the following.

`int "dx"/(("x" - "x"^2))`= 

Fill in the Blank.

`int (5("x"^6 + 1))/("x"^2 + 1)` dx = x⁴ + ______ x³ + 5x + c

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

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 ______.

Fill in the Blank.

`int 1/"x"^3 [log "x"^"x"]^2 "dx" = "P" (log "x")^3` + c, then P = _______

State whether the following statement is True or False.

The proper substitution for `int x(x^x)^x (2log x + 1)  "d"x` is `(x^x)^x` = t

State whether the following statement is True or False.

If `int x  "e"^(2x)` dx is equal to `"e"^(2x)` f(x) + c, where c is constant of integration, then f(x) is `(2x - 1)/2`.

State whether the following statement is True or False.

If ∫ x f(x) dx = `("f"("x"))/2`, then find f(x) = `"e"^("x"^2)`

Evaluate:

`int (5x^2 - 6x + 3)/(2x − 3)` dx

Evaluate `int (5"x" + 1)^(4/9)` dx