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Grade 12Integral Calculus

Calculate the area bounded by
f(x) = x² – x from x = 0 to 2.

Lovey

11 Years agoGrade 12

1 Answer

Jitender Singh

11 Years ago

Ans:
Hello Student,
Please find answer to your question below

f(x) = x^2 – x
Area ‘A’
$A = |\int_{0}^{1}(x^2-x)dx| + \int_{1}^{2}(x^2-x)dx$
$A = |(\frac{x^3}{3}-\frac{x^2}{2})_{0}^{1}| + \int_{1}^{2}(x^2-x)dx$
$A = |(\frac{1}{3}-\frac{1}{2})| + \int_{1}^{2}(x^2-x)dx$
$A = |-\frac{1}{6}| + \int_{1}^{2}(x^2-x)dx$
$A = \frac{1}{6} + (\frac{x^3}{3}-\frac{x^2}{2})_{1}^{2}$
$A = \frac{1}{6} + [(\frac{8}{3}-\frac{2^2}{2})-(\frac{1}{3}-\frac{1}{2})]$
$A = \frac{1}{6} + [\frac{2}{3}-(-\frac{1}{6})]$
$A = \frac{1}{6} + [\frac{4}{6}+\frac{1}{6})]$
$A = \frac{1}{6} + \frac{5}{6}$
$A = 1$

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