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08/02/2022 2:51 pm
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If x φ(x) = \(\int_5^x\)(3t2 - 2φ'(t))dt, x > -2, and φ(0) = 4, then φ(2) is .........
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08/02/2022 2:56 pm
x φ(x) = \(\int_5^x\)(3t2 - 2φ'(t))dt
xφ(x) = x3 -125 - 2[φ(x) - φ(5)]
xφ(x) = x3 -125 - 2φ(x) - 2φ(5)
φ(0) = 4 ⇒ φ(5) = -\(\frac{133}{2}\)
φ(x) = \(\frac{x^3 + 8}{x+2}\)
φ(2) = 4