" 3."int_(0)^(a)f(x)dx=

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):}

Prove that : int_(0)^(2a) f(x)dx=int_(0)^(a) f(x)dx+int_(0)^(a) f(x)dx+int_(0)^(a) f(2a-x)dx

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

prove that : int_(0)^(2a) f(x)dx = int_(0)^(a) f(x)dx + int_(0)^(a)f(2a-x)dx

int_(0)^(a)f(2a-x)dx=m and int_(0)^(a)f(x)dx=n then int_(0)^(2a)f(x)dx is equal to

int_(0)^(a)f(x)dx=lambda and int_(0)^(a)f(2a-x)dx=mu then int_(0)^(2a)f(x) dx is equal to

If int_(0)^(a)f(2a-x)dx = m and int_(0)^(a)f(x) dx = n , then int_(0)^(2a)f(x)dx is equal to

Prove that int_(0)^(2a)f(x)dx=int_(0)^(a)[f(a-x)+f(a+x)]dx

Prove that int_(0)^(2a)f(x)dx=int_(0)^(a)[f(a-x)+f(a+x)]dx

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