Question

find the area of the region bounded by the curve y=x2 and line y=4​

Answer 1

Answer:

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Answer 2

Explanation:

y. = x^2……………….(1).

y. = x……………………..(2).

From eqn. (1) and (2).

x^2. = x.

or. x^2. - x = 0

or. x.(x-1) =0. =>. x= 0. , 1.

But y. = x. => y = 0. , 1.

Thus , (0,0) and (1,1) are the point of intersection.

Area between (y=x and y=x^2) = integ. (0 to 1) of | (x - x^2).dx |.

= (0 to 1) of. | (x^2)/2. - (x^3)/3 |.

= | (1/2–1/3) - (0 - 0) |

= | (1/6) - (0) |.

= 1/6 sq.unit.