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

`int logx/x  "d"x`

`int (2 + cot x - "cosec"^2x) "e"^x  "d"x`

`int "e"^x[((x + 3))/((x + 4)^2)] "d"x`

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

`int x^x (1 + logx)  "d"x`

`int 1/(xsin^2(logx))  "d"x`

`int sqrt(x)  sec(x)^(3/2) tan(x)^(3/2)"d"x`

`int (cos2x)/(sin^2x)  "d"x`

`int cot^2x  "d"x`

`int x/(x + 2)  "d"x`

`int cos^7 x  "d"x`

`int(log(logx))/x  "d"x`

`int sqrt(("e"^(3x) - "e"^(2x))/("e"^x + 1))  "d"x`

The area of the region bounded by the curve y = sinx, X-axis and the lines x = 0, x = 4π is ______ sq.units

The area of the region bounded by the ellipse x²/64 + y²/100 = 1, is ______ sq.units

The area bounded by the parabola y² = x along the X-axis and the lines x = 0, x = 2 is ______ sq.units

The area bounded by the curve y² = x², and the line x = 8 is ______

The area bounded by the parabola y² = 32x the X-axis and the latus rectum is ______ sq.units

The area bounded by the ellipse `x^2/4 + y^2/25` = 1 and the line `x/2 + y/5` = 1 is ______ sq.units

The area enclosed by the line 2x + 3y = 6 along X-axis and the lines x = 0, x = 3 is ______ sq.units