Question Detail

MTH 102 MTH 102 Past Questions Objective Question
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Question

Evaluate ∫₀^π (cosx - 2x) dx.
Options
A <code>-2(1 - π²)</code>
B <code>-π²</code>
Correct Answer
C <code>-2(1 - 2π²)</code>
D <code>π²</code>
Correct Answer

Option B is the correct answer.

Detailed Explanation

To evaluate the definite integral ∫₀^π (cosx - 2x) dx, we first find the antiderivative of the integrand:
  1. Integrate cosx:∫ cosx dx = sinx
  2. Integrate -2x:∫ -2x dx = -x²
  3. The antiderivative is sinx - x².
  4. Evaluate the definite integral using the Fundamental Theorem of Calculus:[sinx - x²]₀^π = (sin(π) - π²) - (sin(0) - 0²)= (0 - π²) - (0 - 0)= -π²
The value of the definite integral is -π².

Hint

Find the antiderivative of each term in the integrand separately, then apply the limits of integration. Remember that sin(π) = 0 and sin(0) = 0.

Question Info

Course: MTH 102
Topic: MTH 102 Past Questions
Type: Objective
Difficulty: Not specified
Question 431 of 930
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