Coordinate of P is (1,1) and the coordinate of Q is (2,0). What is the area of the area bounded by the curve $y=2x-x^2$ , the straight line $x+y=2$ and the y-axis?

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Coordinate of P is (1,1) and the coordinate of Q is (2,0). What is the area of the area bounded by the curve $y=2x-x^2$ , the straight line $x+y=2$ and the y-axis?

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Answer 1 · 2018-03-25T20:51:02

The area is $5/6$ square units.

Explanation:

We want to integrate on $(0, 1)$ . You can see that the linear function is above the quadratic function therefore our area equation will be

$A = int_0^1 2 - x - (2x - x^2) dx$

$A = int_0^1 2 - x -2x + x^2 dx$

$A = int_0^1 x^2 - 3x + 2 dx$

$A = [1/3x^3 - 3/2x^2 + 2x]_0^1$

$A = 1/3(1)^3 - 3/2(1)^2 + 2(1)$

$A = 1/3 - 3/2 + 2$

$A =5/6$

Hopefully this helps!

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Coordinate of P is (1,1) and the coordinate of Q is (2,0). What is the area of the area bounded by the curve $y=2x-x^2$ , the straight line $x+y=2$ and the y-axis?

1 Answer

Explanation:

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Science

Math

Humanities

... and beyond

Coordinate of P is (1,1) and the coordinate of Q is (2,0). What is the area of the area bounded by the curve y=2x-x^2y=2x-x^2, the straight line x+y=2x+y=2 and the y-axis?

1 Answer

Explanation:

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Coordinate of P is (1,1) and the coordinate of Q is (2,0). What is the area of the area bounded by the curve $y=2x-x^2$ , the straight line $x+y=2$ and the y-axis?