`int_(-a)^asqrt((a-x)/(a+x))dx`

int_(-a)^(a)sqrt((a+x)/(a-x))dx

int_(-a)^(a)log((a-x)/(a+x))dx=?

int_(0)^(x)(a^(-x)-b^(-x))dx=

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

int_0^asqrt(a^2 -x^2)dx =

Which of the following is incorrect? int_(a+ c)^(b+c)f(x)dx=int_a^bf(x+c)dx int_(ac)^(b c)f(x)dx=cint_a^bf(c x)dx int_(-a)^af(x)dx=1/2int_(-a)^a(f(x)+f(-x)dx None of these

Which of the following is incorrect? int_(a+ c)^(b+c)f(x)dx=int_a^bf(x+c)dx int_(ac)^(b c)f(x)dx=cint_a^bf(c x)dx int_(-a)^af(x)dx=1/2int_(-a)^a(f(x)+f(-x)dx None of these

Prove that int_(0)^(a) f(x) dx = int_(0)^(a) f(a - x)dx and hence evaluate the following: (a) int_(0)^(a) (sqrt(x))/(sqrt(x) + sqrt(a) - x)dx

int_(-a) ^(a) dx/(x+x^(3)) =

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