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What is the area under the curve y = sin(x) from x = 0 to x = π?
What is the area under the curve y = sin(x) from x = 0 to x = π?
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Practice Questions
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Q1
What is the area under the curve y = sin(x) from x = 0 to x = π?
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The area is given by the integral from 0 to π of sin(x) dx. This evaluates to [-cos(x)] from 0 to π = [1 - (-1)] = 2.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the area under the curve y = sin(x) from x = 0 to x = π?
Solution:
The area is given by the integral from 0 to π of sin(x) dx. This evaluates to [-cos(x)] from 0 to π = [1 - (-1)] = 2.
Steps: 8
Show Steps
Step 1: Understand that we want to find the area under the curve of the function y = sin(x) between x = 0 and x = π.
Step 2: The area under the curve can be found using an integral. We set up the integral as ∫ from 0 to π of sin(x) dx.
Step 3: To solve the integral, we need to find the antiderivative of sin(x). The antiderivative of sin(x) is -cos(x).
Step 4: Now we evaluate the integral from 0 to π. This means we will calculate -cos(π) - (-cos(0)).
Step 5: Calculate -cos(π). Since cos(π) = -1, we have -(-1) = 1.
Step 6: Calculate -cos(0). Since cos(0) = 1, we have -1.
Step 7: Now combine the results: 1 - (-1) = 1 + 1 = 2.
Step 8: Therefore, the area under the curve y = sin(x) from x = 0 to x = π is 2.
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