JEE Main 2019 · 8 April · Shift II

JEE Main 2019 Mathematics question on Definite Integrals and Areas

Let f(x)=∫0xg(t)dtf(x) = \int\limits_0^x g(t)dt, where gg is a non-zero even function. If f(x+5)=g(x)f(x+5) = g(x), then ∫0xf(t)dt\int\limits_0^x f(t)dt equals
  1. A.
    5∫5x+5g(t)dt5\int\limits_5^{x+5} g(t)dt
  2. B.
    ∫5x+5g(t)dt\int\limits_5^{x+5} g(t)dt
  3. C.
    2∫5x+5g(t)dt2\int\limits_5^{x+5} g(t)dt
  4. D.
    ∫x+55g(t)dt\int\limits_{x+5}^5 g(t)dt
Show answer

Correct option: D

[JEE Main 2019 · 8 April · Shift II]

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