which of the following is TRUE ?(A) `x*int(dx)/x=xln|x|+C`

Which one of the following is FALSE? (A)x.int(1)/(x)dx=x ln|x|+C(B)x.int(1)/(x)dx=x.ln|x|+Cx

Which of the following is true ?(A)int_(0)^(1)e^(x^(2))dx =e(C)1 =e(D) 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

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)^(b)f(x+c)dxint_(a+c)^(bc)f(x)dx=c int_(a)^(b)f(cx)dxint_(-ac)^(a)f(x)dx=(1)/(2)int_(-a)^(a)(f(x)+f(-x)dx None of these

Which of the following are true ?(i)int_(a)^( pi-a)xf(sin x)dx=(pi)/(2)int_(a)^( pi-a)f(sin x)dx( ii) int_(-a)^(a)f(x^(2))dx=2int_(0)^(a)f(x^(2))dx( iii) int_(0)^(n pi)f(cos^(2)x)dx=n int_(0)^( pi)f(cos x)dx,n in N (iv) int_(0)^(b-c)f(x+c)dx=int_(c)^(b)f(x)dx

Which of the following is true Statement-I : int_(0)^(2pi) sqrt((1-cos2x)/(2)) dx=4 Statement-II : int_(-1)^(1) log((1+x)/(1-x))dx= 2 int_(0)^(1) log (1+ x)/(1-x)dx