HSC Commerce: Marketing and Salesmanship 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Evaluate the following.

`int (log "x")/(1 + log "x")^2` dx

`int ("x" + 1/"x")^3 "dx"` = ______

Choose the correct alternative from the following.

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

Choose the correct alternative from the following.

`int (1 - "x")^(-2) "dx"` = 

Choose the correct alternative from the following.

`int (("x"^3 + 3"x"^2 + 3"x" + 1))/("x + 1")^5  "dx"` = 

Evaluate: Find the primitive of `1/(1 + "e"^"x")`

Evaluate: `int ("ae"^("x") + "be"^(-"x"))/("ae"^("x") - "be"^(−"x"))` dx

Evaluate: `int "dx"/sqrt(4"x"^2 - 5)`

Evaluate: `int "dx"/(3 - 2"x" - "x"^2)`

Evaluate: `int "dx"/("9x"^2 - 25)`

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

Evaluate: `int "dx"/("x"[(log "x")^2 + 4 log "x" - 1])`

Evaluate: `int "dx"/(5 - 16"x"^2)`

Evaluate: `int "dx"/(25"x" - "x"(log "x")^2)`

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

Evaluate:

∫ (log x)² dx

Find the area of the region bounded by the following curves, the X-axis and the given lines:  y = x⁴, x = 1, x = 5

Find the area of the region bounded by the following curves, the X-axis, and the given lines:

y = `sqrt(6x + 4), x = 0, x = 2`

Find the area of the region bounded by the following curves, the X-axis and the given lines: y = `sqrt(16 - x^2)`, x = 0, x = 4

Find the area of the region bounded by the following curves, the X-axis and the given lines:  2y = 5x + 7, x = 2, x = 8