Question
Question: If I = \(\int_{- 3}^{2}{(|x + 1| + ⥂ |x + 2|} + |x - 1|)dx\), then I equals:...
If I = ∫−32(∣x+1∣+⥂∣x+2∣+∣x−1∣)dx, then I equals:
A
231
B
235
C
237
D
239
Answer
231
Explanation
Solution
We can write
I = I1 + I2 + I3
where I1 = ∫−32∣x+1∣dx etc.
Put x + 1 = t, so that
I1 = ∫−23∣t∣dt =∫−20(−t)dt + ∫03tdt
= – 21t2]−20 + 21t2]03= 213
Similarly, I2 = I3 = 29
Thus, I = 231