jee-main 2021 Q89

jee-main · India · session2_16mar_shift1 Indefinite & Definite Integrals Integral Equation with Symmetry or Substitution

Let $f : R \rightarrow R$ be a continuous function such that $f ( x ) + f ( x + 1 ) = 2$ for all $x \in R$. If $I _ { 1 } = \int _ { 0 } ^ { 8 } f ( x ) d x$ and $I _ { 2 } = \int _ { - 1 } ^ { 3 } f ( x ) d x$, then the value of $I _ { 1 } + 2 I _ { 2 }$ is equal to $\_\_\_\_$.

Let $f : R \rightarrow R$ be a continuous function such that $f ( x ) + f ( x + 1 ) = 2$ for all $x \in R$. If $I _ { 1 } = \int _ { 0 } ^ { 8 } f ( x ) d x$ and $I _ { 2 } = \int _ { - 1 } ^ { 3 } f ( x ) d x$, then the value of $I _ { 1 } + 2 I _ { 2 }$ is equal to $\_\_\_\_$.

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