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What is the area under the curve y = sin(x) from x = 0 to x = π?

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Question: What is the area under the curve y = sin(x) from x = 0 to x = π?

Options:

  1. 1
  2. 2
  3. π
  4. 0

Correct Answer: 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.

What is the area under the curve y = sin(x) from x = 0 to x = π?

Practice Questions

Q1
What is the area under the curve y = sin(x) from x = 0 to x = π?
  1. 1
  2. 2
  3. π
  4. 0

Questions & Step-by-Step Solutions

What is the area under the curve y = sin(x) from x = 0 to x = π?
Correct Answer: 2
  • 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.
  • Definite Integral – The concept of calculating the area under a curve using definite integrals.
  • Trigonometric Functions – Understanding the properties and behavior of the sine function over a specified interval.
  • Fundamental Theorem of Calculus – Applying the fundamental theorem to evaluate the integral of a function.
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