Thinkwell | Exercise_2.101.pdf - Thinkwell | Exercise 8:47 PM back 4 of 8 What is the area bound by the curves 1 1 y = \u2212 x 2 x = \u22123 x = \u22121 and the

Thinkwell | Exercise_2.101.pdf - Thinkwell | Exercise 8:47...

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Unformatted text preview: Thinkwell | Exercise 10/27/19, 8:47 PM back 4 of 8 What is the area bound by the curves 1 1 y = − x + 2 , x = −3, x = −1, and the x x-axis? Correct! next You said C: 2 + ln 3 3 The correct answer is C: 2 + ln 3 3 Explanation: Start by constructing the definite integral. Then take the antiderivative and evaluate. −1 ⎛ 1 1 ⎞ A=∫ − + dx −3 ⎝ x x2 ⎠ =∫ −1 −3 (−x−1 + x−2 ) dx −1 = (− ln ∣x∣ − x−1 )∣∣−3 −1 −1 = (− ln ∣∣ − 1∣∣ − (−1) ) − (− ln ∣∣ − 3∣∣ − (−3) ) = (− ln 1 + 1) − (− ln 3 + = 0 + 1 + ln 3 − = back answer key 1 ) 3 1 3 2 + ln 3 3 next Page 1 of 1 ...
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