JEE MAIN - Mathematics (2021 - 31st August Morning Shift - No. 22)
If $$x\phi (x) = \int\limits_5^x {(3{t^2} - 2\phi '(t))dt} $$, x > $$-$$2, and $$\phi$$(0) = 4, then $$\phi$$(2) is __________.
Answer
4
Explanation
$$x\phi (x) = \int\limits_5^x {3{t^2} - 2\phi '(t)dt} $$
$$x\phi (x) = {x^3} - 125 - 2[\phi (x) - \phi (5)]$$
$$x\phi (x) = {x^3} - 125 - 2\phi (x) - 2\phi (5)$$
$$\phi (0) = 4 \Rightarrow \phi (5) = {{133} \over 2}$$
$$\phi (x) = {{{x^3} + 8} \over {x + 2}}$$
$$\phi (2) = 4$$
$$x\phi (x) = {x^3} - 125 - 2[\phi (x) - \phi (5)]$$
$$x\phi (x) = {x^3} - 125 - 2\phi (x) - 2\phi (5)$$
$$\phi (0) = 4 \Rightarrow \phi (5) = {{133} \over 2}$$
$$\phi (x) = {{{x^3} + 8} \over {x + 2}}$$
$$\phi (2) = 4$$
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