HSC Science (General) इयत्ता १२ वी - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Evaluate:

`int_0^(pi/2) cos^3x  dx`

Evaluate: `int_0^pi cos^2 x  "d"x`

Evaluate: `int_0^(pi/4) (tan^3x)/(1 + cos 2x)  "d"x`

Evaluate: `int_0^(pi/4)  cosx/(4 - sin^2 x)  "d"x`

Evaluate: `int_1^3 (cos(logx))/x  "d"x`

Evaluate: `int_0^(pi/2) (sin^2x)/(1 + cos x)^2 "d"x`

Evaluate: `int_0^9 sqrt(x)/(sqrt(x) + sqrt(9 - x)  "d"x`

Evaluate: `int_0^(pi/2) (sin^4x)/(sin^4x + cos^4x)  "d"x`

Evaluate: `int_3^8 (11 - x)^2/(x^2 + (11 - x)^2)  "d"x`

Evaluate: `int_(-1)^1 |5x - 3|  "d"x`

Evaluate: `int_(-4)^2 1/(x^2 + 4x + 13)  "d"x`

Evaluate: `int_0^1 1/sqrt(3 + 2x - x^2)  "d"x`

Evaluate: `int_0^1 x* tan^-1x  "d"x`

Evaluate: `int_0^(1/sqrt(2)) (sin^-1x)/(1 - x^2)^(3/2)  "d"x`

Evaluate: `int_0^(pi/4) sec^4x  "d"x`

Evaluate: `int_0^(pi/2) 1/(5 + 4cos x)  "d"x`

Evaluate: `int_0^(pi/2) cos x/((1 + sinx)(2 + sinx))  "d"x`

Evaluate: `int_(-1)^1 1/("a"^2"e"^x + "b"^2"e"^(-x))  "d"x`

Evaluate: `int_0^"a" 1/(x + sqrt("a"^2 - x^2))  "d"x`

Evaluate: `int_0^3 x^2 (3 - x)^(5/2)  "d"x`