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Find the value of ∫_0^π sin(x) dx.
Find the value of ∫_0^π sin(x) dx.
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Practice Questions
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Q1
Find the value of ∫_0^π sin(x) dx.
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∫_0^π sin(x) dx = [-cos(x)] from 0 to π = -(-1 - 1) = 2.
Questions & Step-by-step Solutions
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Q
Q: Find the value of ∫_0^π sin(x) dx.
Solution:
∫_0^π sin(x) dx = [-cos(x)] from 0 to π = -(-1 - 1) = 2.
Steps: 6
Show Steps
Step 1: Identify the integral you need to solve: ∫_0^π 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 ∫_0^π sin(x) dx is 2.
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