How do you find the area bounded by the x axis, y axis and x+y=4?

Answer 1

Calculus

y = -x+4

so we have to find the intersection. They "y axis" means that x = 0, so that is the lower bound of the integral. To find the upper bound, we have to find where y=-x+4 crosses the x axis. That occurs when x = 4.

So we can set up the integral: #int_0^4 (-x+4) dx# which is #[-0.5x^2 + 4x]_0^4# which is 8.

That should be the answer I think.

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Answer 2

To find the area bounded by the x-axis, y-axis, and the line (x+y=4), you need to first identify the vertices of the triangle formed by these boundaries. Then, you can use geometry to calculate the area of this triangle.

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Answer 3

To find the area bounded by the x-axis, y-axis, and the line (x + y = 4), you would follow these steps:

  1. Determine the points where the line intersects the axes by setting each axis to zero:

    • When (x = 0), (y = 4)
    • When (y = 0), (x = 4)
  2. Plot these points on the coordinate plane.

  3. Draw the line (x + y = 4) on the coordinate plane, connecting the points where it intersects the axes.

  4. The area bounded by the x-axis, y-axis, and the line (x + y = 4) forms a triangle.

  5. Calculate the area of this triangle using the formula for the area of a triangle: (A = \frac{1}{2} \times \text{base} \times \text{height}).

    In this case, you can take either the x-axis or the y-axis as the base, and the other axis as the height.

  6. Substitute the values into the formula and calculate the area.

So, you find the area bounded by the x-axis, y-axis, and the line (x + y = 4) by calculating the area of the triangle formed by these elements.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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