IIT JEE INTEGRALS If `f(t)` is an odd function, then `varphi(x)=int_a^xf(t)dt` is an even funct...

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If f(t) is an odd function , then prove that integral a to x f(t) dt will be an even function If f(t) is an odd function , then prove that integral a to x f(t) dt will be an even function
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if f(x) = integral 0 to x f(t) dt and integral 0 to 1 1/f(t) dt =sqrt(2) then find f(x) if f(x) = integral 0 to x f(t) dt and integral 0 to 1 1/f(t) dt =sqrt(2) then find f(x)
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