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

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

Find the area of the region bounded by the following curves, the X-axis and the given lines: 2y + x = 8, x = 2, x = 4

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

y = x² + 1, x = 0, x = 3

Find the area of the region bounded by the following curve, the X-axis and the given line:

y = 2 – x², x = –1, x = 1

Find the area of the region bounded by the parabola y² = 4x and the line x = 3.

Choose the correct alternative :

Area of the region bounded by the curve x² = y, the X-axis and the lines x = 1 and x = 3 is _______.

The area of the region bounded by y² = 4x, the X-axis and the lines x = 1 and x = 4 is _______.

Area of the region bounded by x² = 16y, y = 1 and y = 4 and the Y-axis, lying in the first quadrant is _______.

Choose the correct alternative :

Area of the region bounded by y = x⁴, x = 1, x = 5 and the X-axis is _____.