HSC Commerce (Marathi Medium) 12th Standard Board Exam [इयत्ता १२ वी] - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

`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 - 1)"d"x)/((x + 1)(x - 2))` = A log|x + 1|  + B log|x – 2|, then A + B = 1

Evaluate `int 1/(x(x - 1))  "d"x`

Evaluate `int 1/(x log x)  "d"x`

Evaluate `int 1/(4x^2 - 1)  "d"x`

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

`int "e"^x x/(x + 1)^2  "d"x`

`int logx/(1 + logx)^2  "d"x`

`int 1/sqrt(x^2 - 8x - 20)  "d"x`

Choose the correct alternative:

Area of the region bounded by the curve y = x³, x = 1, x = 4 and the X-axis is ______

Choose the correct alternative:

Using the definite integration area of the circle x² + y² = 16 is ______

Area of the region bounded by the curve x = y², the positive Y axis and the lines y = 1 and y = 3 is ______

Choose the correct alternative:

Area of the region bounded by the curve x² = 8y, the positive Y-axis lying in the first quadrant and the lines y = 4 and y = 9 is ______

Choose the correct alternative:

Area of the region bounded by y² = 16x, x = 1 and x = 4 and the X axis, lying in the first quadrant is ______

Choose the correct alternative:

Area of the region bounded by x = y⁴, y = 1 and y = 5 and the Y-axis lying in the first quadrant is ______

Choose the correct alternative:

Area of the region bounded by the parabola y² = 25x and the lines x = 5 is ______

State whether the following statement is True or False:

The area of portion lying below the X axis is negative

State whether the following statement is True or False:

The area bounded by the curve y = f(x) lies on the both sides of the X-axis is `|int_"a"^"b" "f"(x)  "d"x| + |int_"b"^"c" "f"(x)  "d"x|`

State whether the following statement is True or False:

The equation of the area of the circle is `x^2/"a"^2 + y^2/"b"^2` = 1

The area of the shaded region bounded by two curves y = f(x), and y = g(x) and X-axis is `int_"a"^"b" "f"(x) "d"x + int_"a"^"b" "g"(x)  "d"x`