`int_(a+c)^(b+c) f(x)dx `is equal to

If f(x)=f(a+b-x), then int_(a)^(b) xf(x)dx is equal to

If f(a+b-x) =f(x) , then int_(a)^(b) x f(x) dx is equal to

int_(2-a)^(2+a)f(x)dx is equal to [where f(2-alpha)=f(2+alpha) AAalpha in R (a) 2 int_2^(2+a)f(x)dx (b) 2int_0^af(x)dx (c) 2int_2^2f(x)dx (d) none of these

int_(2-a)^(2+a)f(x)dx is equal to [where f(2-alpha)=f(2+alpha) AAalpha in R (a) 2 int_2^(2+a)f(x)dx (b) 2int_0^af(x)dx (c) 2int_2^2f(x)dx (d) none of these

Let a gt 0 and f(x) is monotonic increase such that f(0)=0 and f(a)=b, "then " int_(0)^(a) f(x) dx +int_(0)^(b) f^(-1) (x) dx is equal to

If f(a+x)=f(x), then int_(0)^(na) f(x)dx is equal to (n in N)

Let f (x) be a conitnuous function defined on [0,a] such that f(a-x)=f(x)"for all" x in [ 0,a] . If int_(0)^(a//2) f(x) dx=alpha, then int _(0)^(a) f(x) dx is equal to

If f(a+b-x)=f(x),\ t h e n\ int_a^b xf(x)dx is equal to a. (a+b)/2int_a^bf(b-x)dx b. (a+b)/2int_a^bf(b+x)dx c. (b-1)/2int_a^bf(x)dx d. (a+b)/2int_a^bf(x)dx

If f(a+b+1-x)=f(x) , for all x where a and b are fixed positive real numbers, the (1)/(a+b) int_(a)^(b) x(f(x)+f(x+1) dx is equal to :

Let f: R->R be a continuous function and f(x)=f(2x) is true AAx in Rdot If f(1)=3, then the value of int_(-1)^1f(f(x))dx is equal to (a)6 (b) 0 (c) 3f(3) (d) 2f(0)