" 18."int_(-5)^(0)f(x)dx," where "f(x)=|x|+|x+2|+|x+5|

Evaluate: int_(-5)^(0)f(x)dx" where "f(x)=|x|+|x+2|+|x+5|

int_(0)^(3)f(x)dx, where f(x)=|x|+|x-1|+|x-2|

int_(-1)^(2)f(x)dx " where " f(x) = |x+1| +|x|+ |x-1| is equal to

int_(0)^(2) f(x) dx = …... , where f(x) = max {x, x^(2) } .

Prove that int_(0)^(2a) f(x) dx = 2int_(0)^(a) f(x) dx when f(2a -x) = f(x) and hence evaluate int_(0)^(pi) |cos x| dx .

int_(0) ^(1) x f ''(x) dx, where f (x) = cos (tan ^(-1)x)

Let f(x) and g(x) be any two continuous function in the interval [0, b] and 'a' be any point between 0 and b. Which satisfy the following conditions : f(x)=f(a-x), g(x)+g(a-x)=3, f(a+b-x)=f(x) . Also int_(0)^(a)f(x)dx=int_(0)^(a)f(a-x)dx, int_(a)^(b)f(x)dx=int_(a)^(b)f(x)dx=int_(a)^(b)f(a+b-x)dx If int_(0)^(a//2)f(x)dx=p," then "int_(0)^(a)f(x)dx is equal to

int_(0)^(a)(f(x))/(f(x)+f(a-x))dx=