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Calculate ∫ from 0 to π of sin(x) dx.
Calculate ∫ from 0 to π of sin(x) dx.
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Practice Questions
1 question
Q1
Calculate ∫ from 0 to π of sin(x) dx.
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The integral evaluates to [-cos(x)] from 0 to π = [1 - (-1)] = 2.
Questions & Step-by-step Solutions
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Q
Q: Calculate ∫ from 0 to π of sin(x) dx.
Solution:
The integral evaluates to [-cos(x)] from 0 to π = [1 - (-1)] = 2.
Steps: 6
Show Steps
Step 1: Identify the integral you need to calculate, which is ∫ from 0 to π of sin(x) dx.
Step 2: Find the antiderivative of sin(x). The antiderivative is -cos(x).
Step 3: Evaluate the antiderivative at the upper limit (π): -cos(π) = -(-1) = 1.
Step 4: Evaluate the antiderivative at the lower limit (0): -cos(0) = -1.
Step 5: Subtract the lower limit result from the upper limit result: 1 - (-1) = 1 + 1 = 2.
Step 6: Conclude that the value of the integral ∫ from 0 to π of sin(x) dx is 2.
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