defence exam Agniveer Vayu Group X & XY Mock Test 01/2026 Mathematics Integral Calculus Properties of Definite Integrals
If f and g are continuous functions in [0, 1] satisfying f(x) = f(a − x) and g(x) + g(a − x) = a, then \(\rm \displaystyle\int_0^a\) f(x) . g(x) dx is equal to
1
\(\rm\frac{a}{2}\)
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\(\rm\frac{a}{2} \rm \displaystyle\int_0^a\) f(x) dx
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\(\rm \displaystyle\int_0^a\) f(x) dx
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a\(\rm \displaystyle\int_0^a\) f(x) dx