class 12

Math

Calculus

Application of Integrals

Let $f:[0,∞)→R$be a continuous function such that $f(x)=1−2x+∫_{0}e_{x−t}f(t)dt$for all $x∈[0,∞)$. Then, which of the following statement(s) is (are) TRUE?The curve $y=f(x)$passes through the point $(1,2)$(b) The curve $y=f(x)$passes through the point $(2,−1)$(c) The area of the region ${(x,y)∈[0,1]×R:f(x)≤y≤1−x_{2} }$is $4π−2 $(d) The area of the region ${(x,y)∈[0,1]×R:f(x)≤y≤1−x_{2} }$is $4π−1 $