JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Analyzing +4 | -1

If a function

y=f(x)

such that

f^{\prime}(x)

is continuous function and satisfies

{(f(x))^2} = k + \int_0^x {\left[ {{{\{ f(t)\} }^2} + {{\left\{ {f'(t)} \right\}}^2}} \right]} \,\,dt,\,k \in {R^ + }\mathrm{, }\,\mathrm{then }

View answer and explanation

Correct option: A

f(x)

is an increasing bounded function for all

x \in R

Option A,

f(x)

is an increasing bounded function for all

x \in R

, is correct because solving the differential equation derived from the given equation yields

f(x) = ke^x

, which is an increasing function. However, the solution provided in the original response is incorrect, as

f(x) = ke^x

is unbounded.

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