We are given with the equation
y = e^-9x with the restriction of x <span>≥ 0
If rotated about the x-axis the area of the resulting surface is
A = </span>π ∫ y² dx
Substituing
A = π ∫ (e^-9x)² dx
A = π ∫ e^-18x dx
The limits are from 0 to positive infinity.
Answer:
In order to sketch a parabola, one will typically use the y-intercept, the x-intercepts, and the vertex.
Step-by-step explanation:
In order to sketch a parabola, one will typically use the given equation in standard form,
, and:
- The y-intercept – the point where the parabola crosses the vertical axis – by substituting 0 for all <em>x</em> values in the given equation and solving for <em>y</em>.
- The x-intercepts – the points where the parabola crosses the horizontal axis – by setting the given equation equal to 0 (i.e., <em>y</em> = 0) and finding the factors (or roots).
- The vertex – the point of symmetry where the parabola changes direction and curves up or down – by using
to find the x-coordinate then plugging that value into the given equation to find the y-coordinate.
Answer:

Step-by-step explanation:
Adding 1 to 1x would make it 2x, but only on the numerator.