I=int f^(-1)(x)dx

If int f(x)dx=g(x) then int f^(-1)(x)dx is

Evaluate: if int f(x)dx=g(x), then int f^(-1)(x)dx

If f(x) is an integrable function and f^-1(x) exists, then int f^-1(x)dx can be easily evaluated by using integration by parts. Sometimes it is convenient to evaluate int f^-1(x)dx by putting z=f^-1(x) .Now answer the question.If I_1=int_a^b[f^2(x)-f^2(a)]dx and I_2=int_(f(a))^(f(b)) 2x[b-f^-1(x)]dx!=0 , then I_1/I_2= (A) 1:2 (B) 2:1 (C) 1:1 (D) none of these

Read the following text and answer the followig questions on the basis of the same : inte^(x)[f(x) + f'(x)]dx = int e^(x)f(x)dx + int e^(x) f'(x)dx = f(x)e^(x) - int f'(x)e^(x)dx + int f'(x)e^(x)dx = e^(x)f(x) + c int e^(x)((x-1)/(x^(2)))dx = __________.

Read the following text and answer the followig questions on the basis of the same : inte^(x)[f(x) + f'(x)]dx = int e^(x)f(x)dx + int e^(x) f'(x)dx = f(x)e^(x) - int f'(x)e^(x)dx + int f'(x)e^(x)dx = e^(x)f(x) + c int(x e^(x))/((1+x)^(2))dx = ________.

Read the following text and answer the followig questions on the basis of the same : inte^(x)[f(x) + f'(x)]dx = int e^(x)f(x)dx + int e^(x) f'(x)dx = f(x)e^(x) - int f'(x)e^(x)dx + int f'(x)e^(x)dx = e^(x)f(x) + c int e^(x)(x+1)dx = __________.

f and g be two positive real valued functions defined on [-1,1] such that f(-x)=(1)/(f(x)) and g is an even function with int_(-1)^(1)g(x)dx=1 then I=int _(-1)^(1) f(x)g(x)dx satisfies

The numbers of possible continuous f(x) defined in [0,1] for which I_1=int_0^1f(x)dx=1,I_2=int_0^1xf(x)dx-a ,I_3=int_0^1x^2f(x)dx=a^2i s//a r e 1 (b) oo (c) 2 (d) 0

The numbers of possible continuous f(x) defined in [0,1] for which I_1=int_0^1f(x)dx=1,I_2=int_0^1xf(x)dx-a ,I_3=int_0^1x^2f(x)dx=a^2i s//a r e 1 (b) oo (c) 2 (d) 0

The numbers of possible continuous f(x) defined in [0,1] for which I_1=int_0^1f(x)dx=1,I_2=int_0^1xf(x)dx-a ,I_3=int_0^1x^2f(x)dx=a^2i s//a r e 1 (b) oo (c) 2 (d) 0