Class 12 Applications Of Integrals · Short Answer2 Marksarea_by_integration

Class 12 Maths · Applications Of Integrals · Short Answer #12

Find the geometric area between y=sin x and the x-axis from x=0 to x=2π.

✅ Step-by-Step Solution

Final Answer: \(4\) square units

Sine is nonnegative on [0,π] and nonpositive on [π,2π]. Split at π and take positive strip heights. The strip widths are \(\sin{\left(x \right)}\) for x∈\(\left[0, \pi\right]\); \(- \sin{\left(x \right)}\) for x∈\(\left[\pi, 2 \pi\right]\).
Primitive \(- \cos{\left(x \right)}\), endpoint difference \(2\); Primitive \(\cos{\left(x \right)}\), endpoint difference \(2\).
Therefore the area is \(4\) square units.

[0.5 marks] Sine is nonnegative on [0,π] and nonpositive on [π,2π]. Split at π and take positive strip heights. The strip widths are \(\sin{\left(x \right)}\) for x∈\(\left[0, \pi\right]\); \(- \sin{\left(x \right)}\) for x∈\(\left[\pi, 2 \pi\right]\).
[1 mark] Primitive \(- \cos{\left(x \right)}\), endpoint difference \(2\); Primitive \(\cos{\left(x \right)}\), endpoint difference \(2\).
[0.5 marks] Therefore the area is \(4\) square units.

Practise interactive questions, flashcards, visual mind maps, and timed board tests for Applications Of Integrals.