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Most Important Selected Qs for JEE AdvancedMathematicsDefinite Integration

Let f be a continuous and even function such that ₀^a f(x) d x=10 . If g(x) is a continuous positive function such that g(x) g(-x)=1 and ₀^a g(x) d x=5 , then find the value of _ -a ^a f(x) 1+g(x) d x

Correct answer

10

Step-by-step solution

aligned f(-x) & =f(x), g(x) g(-x)=1 ₀^a f(x) d x & =10 aligned I= _ -a ^a f(x) 1+g(x) d x ...(1) Using King I= _ -a ^a f(-x) 1+g(-x) d x I= _ -a ^a g(x) f(x) d x 1+g(x) ...(2) Eqn. (1) + Eqn. (2) 2 I= _ -a ^a f(x) d x=2 ₀^a f(x) d x I= ₀^a f(x) d x=10

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