Revision - Relations and Functions , I.T.F

Question on I.T.F.

Class 12 Maths Chapter 1 Relations And Functions Important Questions | CBSE Board Quick Revision

STATEMENT 1:int_(a)^(x)f(t)dt is an even function if f(x) is an odd function.STATEMENT 2:int_(a)^(x)f(t)dx is an odd function if f(x) is an even function.

For x epsilonR , and a continuous function f let I_(1)=int_(sin^(2)t)^(1+cos^(2)t)xf{x(2-x)}dx and I_(2)=int_(sin^(2)t)^(1+cos^(2)t)f{x(2-x)}dx . Then (I_(1))/(I_(2)) is

Derive dimensionally the relation s = ut +(1)/(2)f t^(2) .

If the function / satisfies the relation f(x+y)+f(x-y)=2f(x),f(y)AA x,y in R and f(0)!=0 ,then f(x) is an even function f(x) is an odd function If f(2)=a, then f(-2)=a If f(4)=b, then f(-4)=-b

Questions on G.I.F || fractional part function ,trancedental function

G.I.F. , fractional part function

Statement I The function f(x) = int_(0)^(x) sqrt(1+t^(2) dt ) is an odd function and g(x)=f'(x) is an even function , then f(x) is an odd function.

For any x in R, and f be a continuous function Let I_(1) = int _(sin ^(2)x )^(1-cos ^(2)x) tf t (2-t)dt, I_(2) = int _(sin ^(2)x ) ^(1+cos ^(2)x) f (t(2-t))dt, then I_(1)=