HSC Commerce (English Medium) इयत्ता १२ वी - Maharashtra State Board Question Bank Solutions

Choose the correct alternative:

`int ("d"x)/((x - 8)(x + 7))` =

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

`int 1/x  "d"x` = ______ + c

`int 1/(x^2 - "a"^2)  "d"x` = ______ + c

`int"e"^(4x - 3) "d"x` = ______ + c

`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 ______