If f and g are continuous on [0, a] and satisfy f(x) = f(a - x) and g(x) + g(x - a) = 2, then int_0^a f(x)dx is equal to A)int_0^a f(x)dx B)int_0^a f(a-x)dx C)int_0^a f(a-x)g(a-x)dx D)int_0^a g(x)dx

Davin Irwin

Davin Irwin

Answered question

2023-01-21

If f and g are continuous on [0, a] and satisfy f(x) = f(a - x) and g(x) + g(x - a) = 2, then 0 a f ( x ) d x is equal to
A ) 0 a f ( x ) d x
B ) 0 a f ( a x ) d x
C ) 0 a f ( a x ) g ( a x ) d x
D ) 0 a g ( x ) d x

Answer & Explanation

vcalcanofbb

vcalcanofbb

Beginner2023-01-22Added 11 answers

Explanation:
The right answers are
A 0 a f ( x ) d x
B 0 a f ( a x ) d x
C 0 a f ( a x ) g ( a x ) d x
0 a f ( x ) d x = 0 a f ( a x ) d x
0 a f ( x ) g ( x ) d x 0 a f ( a x ) g ( a x ) d x
0 a f ( x ) g ( x ) d x = 0 a f ( a x ) g ( a x ) d x
0 a f ( x ) g ( x ) d x = 2 0 a f ( x ) d x 0 a f ( x ) g ( x ) d x
2 0 a f ( x ) g ( x ) d x = 2 0 a f ( x ) d x
0 a f ( x ) g ( x ) d x = 0 a f ( x ) d x

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