`int_(-1)^(1)x^(3)dx=0`

If int_(-1)^(1)f(x)dx=0 then

Evaluate: int_(0)^(1)|5x-3|dx( ii) int_(0)^( pi)|cos x|dx( iii) int_(-5)^(5)|x-2|dx( iv )int_(-1)^(1)e^(|x|)dx(v)int_(0)^(2)|x^(2)+2x-3|dx(v)int_(1)^(4)(|x-1|+|x-2|+|x-3|)dx( vi) int_(1)^(2)|x^(3)-x|dx

int_(0)^(1)(1-x)^(9)dx=

int_(0)^(1)(1+2x)dx

int_(0)^(1)log(3+x)dx

int_(0)^(1)|3x-1|dx=

show that (a) int_(0) ^(2pi) sin ^(3) x dx = 0 , (b) int_(-1)^(1) e^(-x^(2)) dx = 2 int_(0)^(1) e^(-x^(2)) dx

int_(0)^(1)(x)/(x+1)dx=

If int_(0)^(1)f(x)dx=1, int_(0)^(1)x f(x)dx=a and int_(0)^(1)x^(2)f(x)dx=a^(2) , then : int_(0)^(1)(a-x)^(2)f(x)dx=

If a, b, gt 0 , then int_(1)^(a)(1)/(x)dx + int_(1)^(b)(1)/(x)dx=