Try this beautiful problem from IIT JAM 2018 which requires knowledge of the properties of Definite integral.
Let be positive real number. If
is a continuous and even function defined on the interval
, then
is equal to :-
Definite Integral
Properties of definite Integral
Even function / Odd function
Answer:
IIT JAM 2018, Problem 4
Definite and Integral calculus : R Courant
In this first I will give you the properties we need to solve this problem :
Property 1 :
[Where is continuous on
]
Property 2 : If is an even function i.e.,
then
Can you drive it from here !!!! Give it a try !!!
Let
[Since, is continuous then
]
[Since
is even]
Adding and
we can get some interesting result !!!
Adding and
we get ,
[Since
is even ]
[ANS]
Try this beautiful problem from IIT JAM 2018 which requires knowledge of the properties of Definite integral.
Let be positive real number. If
is a continuous and even function defined on the interval
, then
is equal to :-
Definite Integral
Properties of definite Integral
Even function / Odd function
Answer:
IIT JAM 2018, Problem 4
Definite and Integral calculus : R Courant
In this first I will give you the properties we need to solve this problem :
Property 1 :
[Where is continuous on
]
Property 2 : If is an even function i.e.,
then
Can you drive it from here !!!! Give it a try !!!
Let
[Since, is continuous then
]
[Since
is even]
Adding and
we can get some interesting result !!!
Adding and
we get ,
[Since
is even ]
[ANS]