" (i) "int_(-1)^(1)x|x|dx=0

Prove that: int_(-1)^(1)x|x|dx=0

Match the following {:("List - 1","List - II"),("I) "int_(-1)^(1)x|x|dx,"a) "(pi)/(2)),("II) "int_(0)^((pi)/(2))(1+log((4+3sinx)/(4+3cosx)))dx,"b) "int_(0)^((pi)/(2))f(x)dx),("III) "int_(0)^(a)f(x)dx,"c) "int_(0)^(a)[f(x)+f(-x)]dx),("IV) "int_(-a)^(a)f(x)dx,"d) "0),(,"e) "int_(0)^(a)f(a-x)dx):}

int_(0)^(1) x dx

int_(0)^(1) x dx

int_(0)^(1)x e^(x)dx=

Prove that int_(-1)x|x|dx=0

int_(0)^(2)[|x|+|x-1|]dx=

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

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