Let f : [0, ∞) → be a continuous function such that f(x)=1-2 x+ _ 0 ^ x e^ x-t f(t) d t…
Mathematics · JEE Advanced · NTA Exams — Differential Equations
Let f : [0, ∞) → be a continuous function such that \(f(x)=1-2 x+\int_{0}^{x} e^{x-t} f(t) d t\) 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)
- The curve y = f(x) passes through the point (2,−1)
- The area of the region {(x, y)∈[0,1] × :
f(x) ≤ y ≤
- The area of the region {(x, y)∈[0, 1] × :
f(x) ≤ y ≤
Answer
(C) The area of the region ( x , y ) ∈ [0,1] × : f ( x ) ≤ y ≤
Sign up free on Edukali to view the step-by-step worked solution and practice thousands of similar questions.
Related practice questions
- Consider the differential equation e x (ydx – dy) = e –x (ydx + dy). Let y = f(x) be a particular…
- Explanation:tion of the differential equation d y d x + ( x+y 2 )= x-y 2 is
- For the primitive integral equation ydx + y 2 dy = x dy ; x ∈ R , y > 0, y = y ( x ), y (1) = 1, then y (–3)…
- A curve passing through (2, 3) and satisfying the differential equation _ 0 ^ x t y(t) d t = x 2 y (x), (x…
- The Explanation:tion of the differential equation x dx + y dy + x d y-y d x x^ 2 +y^ 2 =0 is
- The Explanation:tion of d y d x = x^ 2 +y^ 2 +1 2 x y satisfying y(1) = 1 is given by
- A solution curve of the differential equation (x^ 2 +x y+4 x+2 y+4 ) d y d x -y^ 2 =0, x>0 passes through the…
- The differential equation representing the family of curves y^ 2 =2 c(x+ c ) , where c is a positive…
More Differential Equations questions · Browse all practice questions