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Area of the region bounded by y = cosx, x = 0, x = π and X-axis is ...sq. units.
- a)3
- b)1
- c)2
- d)4
Correct answer is option 'C'. Can you explain this answer?
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Area of the region bounded by y = cosx, x = 0, x = π and X-axis is .....
Required area = 
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= 2(sinx)x/20= 2(1 - 0)
= 2sq. Units
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Area of the region bounded by y = cosx, x = 0, x = π and X-axis is .....
Solution:
Finding the area of the region bounded by y = cosx, x = 0, x = π and X-axis involves integration.
Step 1: Draw the graph of y = cosx
Step 2: Identify the bounds of integration, which are x = 0 and x = π
Step 3: Set up the integral using the formula for area between a curve and the X-axis:
∫[0, π] cosx dx
Step 4: Integrate using the substitution u = sinx
= ∫[0, 0] sinx dx
= -cosx |[0, π]
= -cosπ + cos0
= 2
Therefore, the area of the region bounded by y = cosx, x = 0, x = π and X-axis is 2 sq. units.
Hence, the correct answer is option (c).
Finding the area of the region bounded by y = cosx, x = 0, x = π and X-axis involves integration.
Step 1: Draw the graph of y = cosx
Step 2: Identify the bounds of integration, which are x = 0 and x = π
Step 3: Set up the integral using the formula for area between a curve and the X-axis:
∫[0, π] cosx dx
Step 4: Integrate using the substitution u = sinx
= ∫[0, 0] sinx dx
= -cosx |[0, π]
= -cosπ + cos0
= 2
Therefore, the area of the region bounded by y = cosx, x = 0, x = π and X-axis is 2 sq. units.
Hence, the correct answer is option (c).
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Area of the region bounded by y = cosx, x = 0, x = π and X-axis is ...sq. units.a)3b)1c)2d)4Correct answer is option 'C'. Can you explain this answer?
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