KVPY 2019 SB SX Exam Previous Papers

© examsiri.com

Question : 18 of 120

Marks: +1, -0

Suppose a continuous function f : [0, ∞)→R satisfies

\f (x) = 2 ∫ ↖{x} ↙{0} \tf(t) dt + 1

for all x ≥ 0. Then f(1) equals

e
e $^{2}$
e $^{4}$
e $^{6}$

Solution:

\f (x) = 2 ∫ ↖{x} ↙{0} \tf(t) dt + 1

⇒

\f'(x) = 2x \f(x)

⇒

{\f'(x) }/{\f(x)}=2x

⇒

ln\f(x) = x^2 + c

⇒

\f(x) = Ke^{x^2}

f(0) = 1 ⇒ f(x) =

e^{x^2}

⇒ f(1) = e

© examsiri.com

Go to Question:

Prev Question

Next Question