If `int_(1)^(a) (a-4x)dx ge 6-5a, a gt 1`, then a equals

int_(-1)^(1)[((x-[x))]dx is equal to

int_(-1)^(1)x|x|dx is equal to

int(x^(5))/(x^(6)+1)dx

If m gt 0, n gt 0 , the definite integral l=int_(0)^(1)x^(m-1)(1-x)^(n-1)dx depends upon the vlaues of m and n and is denoted by beta(m,n) , called the beta function. E.g. int_(0)^(1)x^(4)(1-x)^(5)dx=int_(0)^(1)x^(5-1)(1-x)^(6-1)dx=beta(5, 6) and int_(0)^(1)x^(5//2)(1-x)^(-1//2)dx=int_(0)^(1)x^(7//2-1)(1-x)^(1//2-1)dx=beta((7)/(2),(1)/(2)) . Obviously, beta(n, m)=beta(m, n) . If int_(0)^(n)(1-(x)/(n))^(n)x^(k-1)dx=R beta(k, n+1) , then R is equal to

What is int_(1)^(3) |1-x^(4)| dx equal to ?

If int_(-2)^(5) f(x) dx = 4 and int_(0)^(5) {1+f(x)}dx = 7 , then what is int_(-2)^(0) f(x) dx equal to ?

int(1+x^(5))/(1+x)dx is equal to