`Ifint_a^b(f(x))/(f(a)+f(a+b-x))dx=10 ,t h e n` `b=22 ,a=2` (b) `b=15 ,1=-5` `b=10 ,a=-10` (d) `b=10 ,a=-2`

Ifint_a^b|sinx|dx=8a n dint_0^(a+b)|cosx|dx=9,t h e n a+b=(9pi)/2 (b) |a-b|=4pi a/b=15 (d) int_a^bsec^2x dx=0

If int_a^b(f(x)-3x)dx=a^2-b^2 then the value of f(pi/6) is ___

If f(x) is monotonic differentiable function on [a , b] , then int_a^bf(x)dx+int_(f(a))^(f(b))f^(-1)(x)dx= (a) bf(a)-af(b) (b) bf(b)-af(a) (c) f(a)+f(b) (d) cannot be found

If intsinx d(secx)=f(x)-g(x)+c ,t h e n f(x)=secx (b) f(x)=tanx g(x)=2x (d) g(x)=x

Prove that int_(a)^(b)f(x)dx=(b-a)int_(0)^(1)f((b-a)x+a)dx

For every function f (x) which is twice differentiable , these will be good approximation of int_(a)^(b)f(x)dx=((b-a)/(2)){f(a)+f(b)} , for more acutare results for cin(a,b),F( c) = (c-a)/(2)[f(a)-f( c)]+(b-c)/(2)[f(b)-f( c)] When c= (a+b)/(2) int_(a)^(b)f(x)dx=(b-a)/(4){f(a)+f (b)+2 f ( c) }dx If lim_(t toa) (int_(a)^(t)f(x)dx-((t-a))/(2){f(t)+f(a)})/((t-a)^(3))=0 , then degree of polynomial function f (x) atmost is

If f^(prime)(x)=sqrt(2x^2-1)a n dy=f(x^2),t h e n(dy)/(dx)a tx=1 is 2 (b) 1 (c) -2 (d) none of these

Suppose f(x)=e^(a x)+e^(b x),w h e r ea!=b , and that f^(primeprime)(x)-2f^(prime)(x)-15f(x)=0 for all x . Then the product a b is (a) 25 (b) 9 (c) -15 (d) -9

If fig shows the graph of f(x)=a x^2+b x+c ,t h e n Fig A) a c 0 c) a b >0 d ) a b c<0

Given that f satisfies |f(u)-f(v)|lt=|u-v| for u and v in [a , b]dot Then |int_a^bf(x)dx-(b-a)f(a)|lt= (a) ((b-a))/2 (b) ((b-a)^2)/2 (c) (b-a)^2 (d) none of these