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

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

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
6 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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