The area of the curve x = 2 cos t , y = 2 sin t ( 0 ≤ t ≤ 2 π ) must be

x g ′ − y f ′ = 2 cos t ⋅ 2 cos t + 2 sin t ⋅ 2 sin t = 4. A = 2 1 ∫ 0 2 π 4 d t = 4 π (a circle of radius 2).

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Mathematics - Area Under Curves Question with Solution | TestHub

MathematicsArea Under CurvesArea of Curve along axisMedium2 minQB

MathematicsMediumsingle choice

Passage / Comprehension

If a curve is given by its parametric equations $x = f (t), y = g (t)$ and suppose the derivatives $f^{'} (t)$ and $g^{'} (t)$ are continuous functions on the interval $[t_{1}, t_{2}]$ . If $t_{1}$ and $t_{2}$ are the values of parameter $t$ corresponding respectively to the initial and final position in which the curve can be described as a contour in the positive direction (i.e., figure remains left) then the area described by the curve is $A = - \int_{t_{1}}^{t_{2}} g (t) f^{'} (t) d t = \int_{t_{1}}^{t_{2}} f (t) g^{'} (t) d t = \frac{1}{2} \int_{t_{1}}^{t_{2}} (x g^{'} (t) - y f^{'} (t)) d t$ . Answer the following questions.

The area of the curve $x = 2 cos t, y = 2 sin t (0 \leq t \leq 2 π) must be$

Options:

Answer:

Solution:

$x g^{'} - y f^{'} = 2 cos t \cdot 2 cos t + 2 sin t \cdot 2 sin t = 4. A = \frac{1}{2} \int_{0}^{2 π} 4 d t = 4 π$ (a circle of radius 2).

Stream:JEESubject:MathematicsTopic:Area Under CurvesSubtopic:Area of Curve along axis

⏱ 2mℹ️ Source: QB

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