Let `f(0)=0a n dint_0^2f^(prime)(2t)e^(f(2t))dt=5.t h e nv a l u eoff(4)i s` (a)log 2 (b) log 7 (c) log 11 (d) log 13

Let f(0)=0a n dint_0^2f^(prime)(2t)e^(f(2t))dt=5.t h e nv a l u eoff(4)i s log 2 (b) log 7 (c) log 11 (d) log 13

Iff(x)=x+int_0^1t(x+t)f(t)dt ,t h e nt h ev a l u eof(23)/2f(0) is equal to _________

If f(0)=1,f(2)=3,f(2)=5,t h e nfin dt h ev a l u eof int_0^1xf"(2x)dx

Let f(x)=1/x^2 int_0^x (4t^2-2f'(t))dt then find f'(4)

Ifint_0^(npi)f(cos^2x)dx=kint_0^pif(c0s^2x)dx ,t h e nfin dt h ev a l u ekdot

For all x in (0,1) (a) e^x (b) (log)_e (x+1) (c) sinx>x (d) (log)_e x > x

If int_(0)^(x) f(t)dt=x^2+int_(x)^(1) t^2f(t)dt , then f'(1/2) is

The value of 3^((log)_4 5)-5^((log)_4 3) is 0 (b) 1 (c) 2 (d) none of these

Let f(x)=int_(0)^(x)(e^(t))/(t)dt(xgt0), then e^(-a)[f(x+1)-f(1+a)]=

If f: RvecR be a differen tiable function atg x=0 satisfying f(0)=0a n df^(prime)(0)=1 , then the value of (lim)_(xvec0)1/xsum_(n=1)^oo(-1)^nf(x/n)= e b. -log2 c. 0 d. 1