If x $? (x) = \int_{5}^{x} (3 t^{2} - 2 ?' (t)) d t, x > - 2, a n d ? (0) = 4, t h e n ? (2) i s__________.$

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Raj Pandey | Contributor-Level 9

2 months ago

$x ? (x) = \int_{}^{} (3 t^{2} - 2 ? (t)) d t, x > - 2, B y$ Leibniz theorem

$? (x) + x ?' (x) = 3 x^{2} - 2 ?' (x) \Rightarrow ?' (x) + \frac{? (x)}{x + 2} = \frac{3 x^{2}}{x + 2} . . . . . . . . . . . . . . (i)$

$∴ I . F . = e^{\int \frac{d x}{x + 2}} = x + 2$

Multiplying (i) by I.F. we get,

$∴ ? (x) = \frac{x^{3} + 8}{x + 2}$

$∴ ? (2) = 4$

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If x $? (x) = \int_{5}^{x} (3 t^{2} - 2 ?' (t)) d t, x > - 2, a n d ? (0) = 4, t h e n ? (2) i s__________.$

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If x ? ( x ) = ∫ 5 x ( 3 t 2 − 2 ? ' ( t ) ) d t , x > − 2 , a n d ? ( 0 ) = 4 , t h e n ? ( 2 ) i s _ _ _ _ _ _ _ _ _ _ .

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If x $? (x) = \int_{5}^{x} (3 t^{2} - 2 ?' (t)) d t, x > - 2, a n d ? (0) = 4, t h e n ? (2) i s__________.$