Find-the-area-bounded-the-curves-f-x-x-3-4x-2-3x-and-x-axis-

Question Number 101057 by bemath last updated on 30/Jun/20

Find the area bounded the

curves f (x) = ∣ x^{3} - 4 x^{2} + 3 x ∣ and

x - axis

Answered by john santu last updated on 30/Jun/20

Commented by john santu last updated on 30/Jun/20

Area = \underset{0}{\int^{1}} (x^{3} - 4 x^{2} + 3 x) d x - \underset{1}{\int^{3}} (x^{3} - 4 x^{2} + 3 x) d x

= {[\frac{1}{4} x^{4} - \frac{4}{3} x^{3} + \frac{3}{2} x^{2}]}_{0}^{1} -

{[\frac{1}{4} x^{4} - \frac{4}{3} x^{3} + \frac{3}{2} x^{2}]}_{1}^{3}

= \frac{5}{12} - (\frac{1}{4} (80) - \frac{4}{3} (26) + \frac{3}{2} (8))

= \frac{5}{12} + \frac{104}{3} - 32 = \frac{5}{12} + \frac{8}{3}

= \frac{37}{12} ★

Commented by bemath last updated on 30/Jun/20

thank

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