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What is the area under the curve y = cos(x) from x = 0 to x = π/2?
What is the area under the curve y = cos(x) from x = 0 to x = π/2?
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Practice Questions
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Q1
What is the area under the curve y = cos(x) from x = 0 to x = π/2?
1
0
π/2
2
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The area is given by the integral from 0 to π/2 of cos(x) dx. This evaluates to [sin(x)] from 0 to π/2 = 1 - 0 = 1.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the area under the curve y = cos(x) from x = 0 to x = π/2?
Solution:
The area is given by the integral from 0 to π/2 of cos(x) dx. This evaluates to [sin(x)] from 0 to π/2 = 1 - 0 = 1.
Steps: 8
Show Steps
Step 1: Identify the function we are working with, which is y = cos(x).
Step 2: Determine the interval for which we want to find the area, which is from x = 0 to x = π/2.
Step 3: Set up the integral to find the area under the curve: ∫ from 0 to π/2 of cos(x) dx.
Step 4: Calculate the integral of cos(x), which is sin(x).
Step 5: Evaluate the integral from 0 to π/2 by substituting the limits: sin(π/2) - sin(0).
Step 6: Calculate sin(π/2), which equals 1, and sin(0), which equals 0.
Step 7: Subtract the two results: 1 - 0 = 1.
Step 8: Conclude that the area under the curve from x = 0 to x = π/2 is 1.
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