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Sticky Note
1∫0 (5t² - 2t) dt = _____?
  1. 2/3
  2. -3/2
  3. -2/3
  4. None of these
Explanation

Let's evaluate the definite integral:

∫01(5t2−2t)dt

Step 1: Find the antiderivative (indefinite integral):

∫(5t2−2t)dt=5⋅t33−2⋅t22+C=53t3−t2+C

Step 2: Evaluate from 0 to 1:

[53t3−t2]01=(53(1)3−(1)2)−(53(0)3−(0)2)=(53−1)−(0)=53−33=23

So, the value is 23.

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