Question

The area bounded by the curve y = 2x – x² and the straight line y = –x is given by -

• A.
• B. $\frac { 43 } { 6 }$
• C. $\frac { 35 } { 6 }$
• D. None of these

Answer 1

Answer: (A)

Answer 2

y = 2x – x² .... (1)

y = –x ....(2)

Solving (1) & (2) x = 0; x = 3

Area = $\int _ { 0 } ^ { 3 } \left( y _ { 2 } - y _ { 1 } \right) d x$

= $\int _ { 0 } ^ { 3 } \left[ 2 x - x ^ { 2 } - ( - x ) \right] d x$ = $\int _ { 0 } ^ { 3 } \left( 3 x - x ^ { 2 } \right) d x$