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ch4aika [34]
3 years ago
6

Calculus. Find the area.

Mathematics
2 answers:
matrenka [14]3 years ago
6 0

Answer:

8/3 square units.

Step-by-step explanation:

First, visualize the area. You can refer to the attachment below.

To find the area then, we will integrate y from x = 0 to x = 2. Therefore:

\displaystyle A=\int_0^2x^2\, dx

Integrate:

\displaystyle A=\frac{1}{3}x^3\Big|_{0}^2

Evaluate:

\displaystyle A=\frac{1}{3}[2^3-0^3]=\frac{1}{3}(8)=\frac{8}{3}

The area is 8/3 square units.

Irina18 [472]3 years ago
5 0

Answer:

<em>A = </em>\frac{8}{3}<em> units²</em>

Step-by-step explanation:

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Elan Coil [88]

Answer:

x = 1 - 5t

y = t

z = 1 - 5t

Step-by-step explanation:

For the equation of a line, we need a point and a direction vector. We are given a point (1, 0, 1).

Since the line is suppose to be a tangent to the given curve at the point (1, 0, 1), we need to find a tangent vector for which the curve passes through that point.

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at t = 1, x = e^(-5)cos5

at t = 0, x = 1

y = e^(-5t)sin5t

at t = 1, y = e^(-5)sin5

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z = e^(-5t)

at t = 1, z = e^(-5)

at t = 0, z = 1

Clearly, the only parameter value for which the curve passes through the point (1, 0, 1) is t = 0.

In vector notation, the curve

r(t) = xi + yj + zk

= e^(-5t)cos5t i + e^(-5t)sin5t j + e^(-5t) k

r'(t) = [-5e^(-5t)cos5t - e^(-5t)sin5t] i +[e^(-5t)cos5t - 5e^(-5t)sin5t] j - 5e^(-5t) k

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We get the parametric equation from this.

x = x(0) + tx'(0)

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