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

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

Evaluate `int 1/((2"x" + 3))` dx

Evaluate `int "x - 1"/sqrt("x + 4")` dx

Evaluate: If f '(x) = `sqrt"x"` and f(1) = 2, then find the value of f(x).

Evaluate: ∫ |x| dx if x < 0

Evaluate: `int 1/(2"x" + 3"x" log"x")` dx

Evaluate: `int 1/(sqrt("x") + "x")` dx

Evaluate: `int (2"e"^"x" - 3)/(4"e"^"x" + 1)` dx

Evaluate: `int "e"^"x" (1 + "x")/(2 + "x")^2` dx

Evaluate: `int "x" * "e"^"2x"` dx

Evaluate: `int log ("x"^2 + "x")` dx

Evaluate: `int "e"^sqrt"x"` dx

Evaluate: `int sqrt("x"^2 + 2"x" + 5)` dx

Evaluate: `int sqrt(x^2 - 8x + 7)` dx

Find the area of ellipse `x^2/(4) + y^2/(25)` = 1.