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Mathematics · 2020
JEE Main · 7 January 2020, Shift 1 · Q60
If f( a + b +1-x)=f(x), for all x, where a and b are fixed positive real numbers, then 1/(a + b) ∫_a^b x(f(x)+f(x+1)) d x is equal to:
If $\displaystyle f(\mathrm{a}+\mathrm{b}+1-x)=f(x)$, for all $\displaystyle x$, where a and b are fixed positive real numbers, then $\displaystyle \frac{1}{\mathrm{a}+\mathrm{b}} \int_{\mathrm{a}}^{\mathrm{b}} x(f(x)+f(x+1)) \mathrm{d} x \quad$ is equal to :
Official answer
(1)
$\displaystyle \int_{\mathrm{a}+1}^{\mathrm{b}+1} f(x) \mathrm{d} x$
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JEE Main 2020 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.