JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

The function

f

whose graph passes through

(0,7 / 3)

and whose derivative is

x \sqrt{1-x^2}

is given by

View answer and explanation

Correct option: C

f(x)=-(1 / 3)\left[\left(1-x^2\right)^{3 / 2}-8\right]

Option C (

f(x)=-(1 / 3)\left[\left(1-x^2\right)^{3 / 2}-8\right]

) is correct because integrating

x \sqrt{1-x^2}

and applying the initial condition

f(0) = 7/3

yields the correct function.

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