Question

If the function f(x) is even, then which of the following is zero?
(a)
an
(b) bn
(d) nothing is zero
(C)
a0​

Answer 1

Answer:

a an

Step-by-step explanation:

because is became same answer

Answer 2

The correct answer is option (b) bn.

Explanation:

• If the function f(x) is even, then bn is zero.
• The product of two even functions is always even whereas the product of two odd functions is even.
• So, the product of an even function and an odd function gives an odd function.
• As, Since bn includes sin(nx) term which is an odd function, odd times even function is always odd.
• Therefore, the integral gives zero as the result.
• Hence, the correct answer is option b i.e bn.