JEE MainMathematicsEasyDefinite Integration

The area bounded by the curves y = 6x - x^2 and y = x^2 - 2x
is

Show answer and solution

A = \int_{0}^{4}\mspace{2mu}\left\{ \left( 6x - x^{2} \right) - \left( x^{2} - 2x \right) \right\} dx

A = \int_{0}^{4}\mspace{2mu}\left( 8x - 2x^{2} \right)dx

A = \left\lbrack 4x^{2} - \frac{2}{3}x^{3} \right\rbrack_{0}^{4} = 64 - \frac{128}{3} = \frac{64}{3}

square units

Source: Grass-G / M-13 Mathematics Paper 4 Nov.docx

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